The Roles of Pars Flaccida in Middle Ear Acoustic
Transmission
by
Su Wooi Teoh
B.S., Electrical Engineering
University of Texas at Austin, 1993
Submitted to the Department of Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
a.t the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
January 1996
@
Massachusetts Institute of Technology 1996. All rights reserved.
Author ............
....
... .. .............................................
Depart•
fI
•"
Certine
d1
1
y ..........-....
ent of Electrical Engineering and Computer Science
November 13, 1995
.....
John J. Rosowski
Associate Professor of Otology and Laryngology, Harvard Medical School
Thesis Supervisor
It.
Accepted by ...............
..
.............................
F.R. Morgenthaler
Chairl an, Depart ental Committee on Graduate Students
.IASACAHUSE.iTS INS' iFUTE
OF TECHNOLOGY
APR 111996
LIBRARIES
The Roles of Pars Flaccida in Middle Ear Acoustic Transmission
by
Su W\ooi Teoh
Submitted to the Department of Electrical Engineering and Computer Science
on November 13, 1995, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
This thesis investigates the effect of pars flaccida on the signal transmission properties of the middle ear through acoustic and electro-physiological measurements. Toward
this goal, the middle-ear input admittance, ear-canal to middle-ear sound pressure ratio, and round-window cochlear potential were measured in the ears of twelve gerbils.
Measurements were made before and after various middle ear and tympanic membrane
manipulations, including stiffening or removing the pars flaccida. The results are compared to the predictions of the middle-ear model proposed by Kohlloffel (1984). The
input-admittance measurements show that the pars flaccida can be accurately modeled
by a simple RLC circuit with a resonance at approximately 500 Hz. With the exception
of a small frequency range from 300-600 Hlz, our cochlear potential measurements support
the assumption that the pars flaccida and pars tensa are independent. Within this range,
the pars flaccida acts as a shunt path around the main ossicular transmission pathway.
At frequencies below the pars flaccida resonance, this extra. pathway reduces the ossicular transmission to the inner ear by increasing the middle-ear pressure. These results
suggest that pars flaccida reduces low frequency hearing sensitivity, consistent with the
model prediction. Between 300-600 Hz, significant deviation between the cochlear potential measurements and the model predictions was observed. The cause of this deviation
is unclear and requires further investigations.
Thesis Supervisor: John J. Rosowski
Title: Associate Professor of Otology and Laryngology. Harvard Medical School
Acknowledgments
First and foremost, I would like to extend my most sincere thanks to Dr. John J.
Rosowski, my thesis advisor. John has consistently been the driving force behind this
work.
He has patiently provided intellectual and technical guidance throughout the
project, and has tolerated all the mistakes that I have committed along the way. Through
numerous discussions and meetings, John has patiently corrected my often naive notion
of research and has been an example of a careful and rigorous scientist. Any errors in
this thesis must have been committed in spite of his teaching. I am also greatly indebted
to Professor William T. Peake for introducing me to and teaching me the science of
acoustics and hearing. Without him, this thesis would not have been possible.
Special thanks must go to Deborah Flandermeyer for her help in performing animal
surgeries, proofreading this thesis, and especially for her encouragement in all aspects
of my work. Sunil Puria, Mike Ravicz, and Susan Voss have provided valuable advice
throughout the past year. I thank all members of the Eaton-Peabody Laboratory for
providing such a conducive and comfortable atmosphere for conducting research.
Last but certainly not least, my deepest appreciations go to my sisters and my parents. It is their selfless sacrifice over the years that has made my higher education a
reality.
This work was supported by the MIT Vinton Hayes Fellowship and NIH grant R01
DC 00194.
Contents
1
Introduction
1.1
Brief overview of the hearing process . . . . . . . . . . . . . . . . . . . . . 15
1.2
Overview of the anatomy and functions of the ear . . . . . . . . . . . . . . 16
1.3
Modeling of acoustic systems ................
1.4
2
15
. . . . . . . . . 21
1.3.1
Low frequency circuit analogs . . . . . . . . . . .. . . . . . . . . . 22
1.3.2
High frequency representations of acoustic systems . . . . . . . . . 27
Middle ear models ......................
. . . . . . . . . 28
Methods
37
2.1
Experimental subjects ....................
2.2
Acoustic sources and their characteristics
2.3
. . . . . . . . . 37
. . . . . . . . . . . . . . . . . . 37
. . . . . . . . . 37
2.2.1
Calibration theory ..................
2.2.2
Source description and characteristics
2.2.3
Acoustic loads for source calibration . . . . . . . . . . . . . . . . . 46
2.2.4
Accuracy and limits of acoustic calibration
2.2.5
Level dependency of source characteristics . . . . . . . . . . . . . . 57
Acoustic calibration
2.3.1
.....................
Absolute calibration .................
. . . . . . . . . . . . . . . . 41
. . . . . . . . . . . . . 54
. . . . . . . . . 60
. . . . . . . . . 60
2.3.2
Probe-tube microphone calibration . . . . . . . . . . . . . . . . . . 62
2.4
Stimulus paradigms
2.5
Experimental configuration and procedures
..............................
64
. . . . . . . . . . . . . . . . . 66
2.5.1
Animal preparation
2.5.2
Instrumentation
2.5.3
Cochlear potential measurements . . . . . . . . . . . . . . . . . . .
69
2.5.4
Experimental protocol .........................
71
..........................
66
............................
68
3 Experimental results
3.1
75
Middle-ear input admittance
.........................
75
3.1.1
Correction for ear canal volume . . . . . . . . . . . . . . . . . . . . 77
3.1.2
General features of the measured middle-ear input admittance
3.1.3
Effects of membranal drying on middle-ear input admittance
3.1.4
Input admittance before and after manipulation of pars flaccida
. . 80
. . . 84
---ears with intact bulla ........................
3.1.5
87
Input admittance with and without manipulation to pars flaccida
-- bulla hole open ...........................
3.1.6
Input admittance before and after manipulation of pars flaccida
-- middle ear widely opened
3.1.7
3.2
.....................
92
Effects of removing the pars flaccida "shield" on middle-ear input
admittance
3.1.8
90
. ..
. . . . . . . . . ..
. ..
. ..
. . . . . . . . . . . 94
Pressure measurements in the ear canal and the middle-ear cavity
97
Cochlear potential measurements . . . . . . . . . . . . . . . . . . . . . . . 102
3.2.1
Linearity of cochlear potential measurements
. . . . . . . . . . . . 102
3.2.2
Effects of pars flaccida manipulation on round-window cochlear
potential
4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Discussion
121
4.1
Comparison with previously reported measurements
4.2
Correlation of input admittance measurements with middle ear models . . 125
4.2.1
General considerations .........................
4.2.2
Estimation of model parameters
. . . . . . . . . . . . 121
125
. . . . . . . . . . . . . . . . . . . 129
4.3
Middle-ear pressure levels-model vs measurements
. . . . . . . . . . . . 142
4.4
Effects of Pars Flaccida manipulations on the input to the inner ears bulla wall widely open .............................
4.5
Prediction of the effects of Pars Flaccida manipulations on the input to
the inner ears -
5
145
intact bulla wall
. . . . . . . . . . . . . . . . . . . . . . 153
Summary
163
A Summary of the experimental measurements
165
B Source accuracy charts
169
C Other admittance and pressure measurements
179
D List of symbols
187
List of Figures
1-1
Anatomy of the ear ......................
1-2 Illustrations of a gerbil ear ..................
1-3
Lateral and ventral views of gerbil skull .........
1-4
Circuit representations of lumped acoustic elements.
1-5
A schematic representation of the gerbil middle ear .
1-6
The simple middle ear series model ...........
1-7
Series model that includes the effect of pars flaccida
1-8
Low frequency circuit analog of the middle ear
2-1
Schematic drawing of the acoustic source in a gerbil ear
2-2
Norton-equivalent model of an acoustic source with load
2-3
Cross-sectional diagram of the low frequency source
2-4
Cross-sectional diagram of the high frequency source .
2-5
Internal admittances and normalized volume velocities of the acoustic
sources
2-6
. . .
.
. . . . . . . . . . . . . . . . . . . . . . . . . .
.. . . . . . .
Sound pressure recordings that illustrate the crosstalk artifact in the
acoustic sources ........................................
2-7
Coupling of reference load to the acoustic source ................
. 45
2-8
Cross-sectional diagram of reference loads . . . . . . . . . . . . . . . . . . 49
2-9
Mathematical models of the acoustic loads . . . . . . . . . . . . . . . . . .
2-10 Admittances of reference loads
........................
50
51
2-11 Admittances involved in the calibrations of acoustic sources . . . . . . . . 53
2-12 Comparison of theoretical and measured cavity admittance
. . . . . . . . 55
2-13 Source admittance and volume velocity measurements of hfs at two pressure levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
2-14 Source admittance and volume velocity measurements of lfs at two pressure levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
2-15 The probe tube normalization constant m . . . . . . . . . . . . . . . . . . 63
2-16 Schematic diagram of the experimental setup . . . . . . . . . . . . . . . . 67
2-17 Cochlear potential and impedance measurements obtained from Moller
(1965) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
2-18 Schematic diagram showing the effects of experimental manipulations on
72
the middle ear input admittance YT .....................
3-1
The actual sound pressure levels generated by chirp stimuli in a gerbil ear
canal (B 8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
3-2
Measured and corrected gerbil middle-ear input admittances . . . . . . . .
79
3-3
Input admittance of eight intact gerbil middle ears, Y . . . . . . . . . . ..81
3-4
Input admittance of eight gerbil middle ears opened, YHO ..........
3-5
with the bulla hole left
..................................
83
Effects of membranal drying and moistening on the gerbil middle-ear input
admittance, y HO
...............................
86
3-6
The middle-ear input admittance measured in the right ears of gerbils B8
.
88
and B9--- with the bulla wall intact but the probe-tube hole open . . . . .
91
and B9--- middle ear intact ..
3-7
3-8
.........................
The middle-ear input admittance measured in the right ears of gerbils B8
The middle-ear input admittance measured in the left ears of gerbils B8
and B9--.bulla wall widely opened ......
3-9
... ... .
. . . . .
Effects of removing dental acrylic on the middle-ear input admittance
.
93
. . 96
3-10 Middle-ear cavity to ear-canal pressure ratio measured in the right ears of
gerbils B138 and B9-middle ear intact
...
.. .. ..
. .
. . . . ....
.
98
3-11 Middle-ear cavity to ear-canal pressure ratio measured in the left ears of
.
gerbils B138 and B9-middle ear widely opened . . . . . . . . . . . . . . .101
3-12 Examples of cochlear potential responses to chirp stimuli . . . . . . . . . . 103
3-13 Plots of cochlear potentials versus sound pressure levels before and after
the application of TTX ....
..............
. .
. ..
105
........
3-14 Effects of TTX on the cochlear potential recording . . . . . . . . . . . . . 106
3-15 Stimulus pressure levels and post-TTX cochlear potential responses measured in the left ear of gerbil Bl1 (middle ear widely opened) . . . . . . . 107
3-16 Middle-ear transfer function at various stimulus levels (gerbil Bli)
. . . . 108
3-17 The tone-sweep stimulus spectra and cochlear potential responses measured in the left ear of gerbil BO10 (middle ear widely opened) . . . . . . . 111
3-18 The tone-sweep stimulus spectra and cochlear potential responses measured in the left ear of gerbil B11 (middle ear widely opened) . . . . . . . 112
3-19 Middle-ear input admittance measured in the left ears of gerbils BO10 and
B11 -middle
ear widely opened .
.......
.. ... .
. . . . . .
. 114
3-20 Middle-ear transfer functions of gerbils B10 and B]1 (middle-ear cavity
widely open) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3-21 Changes in middle-ear input admittance, ear-canal sound pressure, and
cochlear potential between pre- and post-stiffened measurements in gerbils
B10 and B11 . ..................................
4-1
119
A comparison of the measured YI and yHO with other available admittance data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4-2
T-test comparison of the similarity between the our measured YI and
yHO with the measurements of Ravicz et al. (1992) . . . . . . . . . . . . 124
4-3
Circuit representation of the series model of the middle ear . . . . . . . . 127
4-4
Comparison of the input admittances YI, YIs, and Y1
measured in
gerbils B8 and B9 with the input admittances of the middle-ear circuit
m odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4-5
Modified "broad-band" middle ear model that allows high frequency representation of the middle-ear input admittance . . . . . . . . . . . . . . . 134
4-6
The ingredients that compose the input admittance of the broadband
middle-ear model, I
4-7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
Comparison of the input admittances YHO and Y H1O measured in gerbils
B8 and B9 with the input admittances of the middle-ear circuit model . . 137
4-8
Comparison of the input admittances yWO and YWO measured in gerbils B8 and B9 with the input admittances of the middle-ear circuit model 139
4-9
Model fit of the middle-ear input admittance of gerbils B10 and B11 yW O and Y•FO ................................
140
4-10 Predictions of middle-ear to ear-canal pressure ratio in the middle ear
intact configuration-circuit model . . . . . . . . . . . . . . . . . . . . . . 143
4-11 Broadband model predictions of middle-ear to ear-canal pressure ratio in
the middle ear intact configuration . . . . . . . . . . . . . . . . . . . . . . 144
4-12 Comparison of the measured cochlear potentials in gerbils B10 and B 11
with the model predictions
..........................
146
4-13 Comparison of the predicted and measured AY,APEc Iv, and ACPIv in
ears with middle ear open ...........................
150
4-14 Comparison of the measured input admittances YWO, model input admittances
F measured
'_WO,
and the middle-ear transfer functions
with the flaccida stiffened ..............................
152
4-15 Comparison of the model and measured CP/UT transfer functions in
gerbils B10 and B11 ...............................
154
4-16 Predictions of the effects of middle-ear cavity and tympanic membrane
manipulations on the middle ear transfer functions (
) of gerbils B10
and B 11 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......
156
4-17 Predictions of the effects of middle-ear cavity and tympanic membrane
manipulations on the transfer function (CP) of gerbils BO and B11 . . . 158
4-18 Predictions of the role of the middle-ear cavity on the effects of stiffening
pars flaccida ..................................
159
- II .
4-19 Effect of using different types of stimulus sources on ACP
. . . . . . . 161
B-1 Source accuracy chart for the low frequency source (driver voltage = 0.32 V)170
B-2 Source accuracy chart for the low frequency source (driver voltage = 0.1 V)171
B-3 Source accuracy chart for the low frequency source (driver voltage = 0.032 V)172
B-4 Source accuracy chart for the low frequency source (driver voltage = 0.01 V)173
B-5 Source accuracy chart for the high frequency source (driver voltage =
0.032 V)........
. . . . . . . . . . . . . . . .o . . . . . .
174
B-6 Source accuracy chart for the high frequency source (driver voltage =
0.01 V) ........
. . . . . . . . . . . . . . . . . . . . . .
175
B-7 Source accuracy chart for the high frequency source (driver voltage =
0.0032 V) .......
B-8 Source accuracy chart
0.001 V)........
. . . . . . . . . . . . . . . . . . . . . .
for the high frequency source (driver
176
voltage =
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
C-1 The middle-ear input admittances measured in the left ear of gerbil A2
180
C-2 The middle-ear input admittances measured in the left ears of gerbils B1
and B2-middle ears widely opened
.....................
181
C-3 The middle-ear input admittances measured in the left ears of gerbils B3
and B5-middle ears widely opened .....................
C-4 Middle-ear cavity to ear-canal pressure ratio measurements
182
. . . . . . . . 183
C-5 Middle-ear cavity to ear-canal pressure ratios measured in the left ears of
gerbils B1 and B2-middle ears widely opened . . . . . . . . . . . . . . . 184
C-6 Middle-ear cavity to ear-canal pressure ratios measured in the left ears of
gerbils B3 and B5-middle ears widely opened . . . . . . . . . . . . . . . 185
List of Tables
2.1
Specifications of the reference loads ...
3.]L
Body weight and ear-canal volume measurements . . . . . . . . . . . . . .
4.1
Middle-ear model parameters .........................
4.2
Middle-ear model parameters ..
4.3
Means and standard deviations of middle-ear model parameters . . . . . . 142
... .. . .
. . . . . . .
. . .
. . . ......
52
77
133
. . . . . . . . . .
.. .
140
Chapter 1
Introduction
1.1
Brief overview of the hearing process
The hearing process in most higher vertebrates begins in the peripheral auditory organs
--- the external and the middle ear. These two structures are responsible for transferring
acoustical vibrations in the external environment to the inner ear, where sensory hair
cells convert the vibrations into neural action potentials. These neural signals are then
conveyed via the auditory nerve and midbrain to the auditory cortex, where the nerve
impulses can be perceived as meaningful sound.
Comprehension of this enormously complex transduction process has been made more
manageable by the divide and conquer approach, where structures along the pathway
are broken down into cascading systems that can be analyzed independently. In this
approach, the analysis of a single stage needs only take into account the overall prefiltering characteristics of the earlier systems and the loading effects of the following
stages, freeing us from many unnecessary secondary details.
At the most peripheral
level, it is common to analyze the external and the middle ear as a single system, with
the inner ear acting as a load. The primary function of the external and middle ear is to
collect and channel sound energy to the inner ear, and in the process filter the frequency
contents of the incoming acoustic signals via passive mechano-acoustic processes 1 . The
inner ear, on the other hand, uses an active mechanical feedback system, producing
hair cell responses that exhibit sharp frequency sensitivity (Zwicker, 1986; Neely and
Kim, 1986; Diependaal et al. , 1987; Pickles, 1988). In addition, the inner ear acts as
a nonlinear mechano-chemical transducer, converting the mechanical vibration of hair
cells into chemical signals that initiate all-or-none neural action potentials.
This thesis is primarily concerned with the modeling of the middle ear. In particular,
it concentrates on the effects of pars flaccida2 in this complex transduction process.
Before we proceed further into the methodology and details of this study, a brief overview
of anatomy and acoustics is in order.
1.2
Overview of the anatomy and functions of the ear
The peripheral auditory system of all mammals can be divided into three regions external, middle, and inner ear. Despite the great variations in size and shape of the
auditory system among different species, several noticeable and important structures
common to all species can be identified in each of the three regions.
Figure 1-1 shows the anatomy of the human auditory system, which illustrates the
important structures observed in most mammals. The outermost portion of the external
ear usually consists of a protruding cartilaginous pinna that functions as a sound collector. The pinna is connected on the medial surface to a funnel-like structure called the
'The stapedius muscle and the tensor tympani muscle may be considered as active elements of the
middle ear, but their effects are mainly felt when subjected to high intensity sound, and they work by
modifying the stiffness of the middle ear, which is a passive mechanical property.
2Pars flaccida is a flaccid region of the tympanic membrane. See Section 1.2 for more details.
16
concha. The narrower end of the concha leads directly to the cartilaginous and bony ear
canal (also called external auditory meatus), which terminates at the tympanic membrane on its medial end. The function of the external ear structures is like that of a horn,
amplifying the gathered sound in a frequency-dependent manner. This amplification is
directionally dependent, and this phenomenon provides cues for directional judgment
(Shaw, 1974).
The tympanic membrane forms the boundary between the middle and the external
ear. Attached to the medial side of the tympanic membrane is the malleus. Together
with incus and stapes, they form the ossicular bones of the middle ear. These three bones
are suspended by ossicular ligaments in the middle ear and act as a connecting bridge,
conducting mechanical vibrations of the tympanic membrane to the fluid-filled cochlea
of the inner ear. One feature of the coupling between malleus and tympanic membrane
deserves further elaboration. In some mammals, such as cat and guinea pig, the entire
tympanic membrane is stiff and firm. The tensa and the tightly coupled malleus form
an efficient pressure transformer (Tonndorf and Khanna, 1970), such that a large part
of the acoustic power received by the tympanic membrane is converted into mechanical
vibrations of the ossicular bones, which then act as the inner ear input (Rosowski et al.
, 1986). While this has been the conventional thought about the function of tympanic
mnembrane and ossicular bones, it is not entirely accurate for many mammals, including
gerbil, mouse, rat, deer, pig, and goat. In these mammals, the tympanic membrane
consists of two distinct parts: the pars tensa and the parsflaccida (also called Shrapnell's
membrane). Figure 1-2b shows the inferior lateral view of a gerbil tympanic membrane,
which illustrates the clear geometrical differences between the pars flaccida and the pars
tensa. The firm pars tensa is the site of attachment for the malleus, similar to the
Stapedius
Tensor
\
Incus
Tympanic
membrane
Figure 1-1: Anatomy of the ear. Sketch of the external, middle, and inner ear of human.
The boxed region shows the detailed middle ear structures. From Atlas of the Ear by
Scanning Electron Microscopy, by Y. Harada, 1983.
tympanic membrane of the cat and human discussed above.
The soft pars flaccida,
however, is loosely coupled to the tympanic ring and the pars tensa; thus, motion of the
flaccida does not elicit any significant mallear movement and transfers little power to
the inner ear. The exact function of pars flaccida is unclear, and is the subject of this
thesis.
All the middle ear structures are housed in an air-filled middle-ear cavity. The cavity
is connected by the Eustachian tube to the nasal-pharyngeal air space. Opening the
tube eliminates any static pressure difference between the middle ear and the external
environment.
Other important structures in the middle ear are the two middle ear
muscles. The stapedius muscle is the smallest striated muscle of the body. It arises
within the posterior wall of the middle ear cavities and inserts onto the neck of the
stapes (Figure 1-1). The other muscle, the tensor tympani, is attached to the malleus
near the tympanic membrane. Contraction of these muscles can alter the stiffness of the
ossicular chain, thus affecting the transmission properties of the middle ear (Pang and
Peake, 1985).
The last component of the peripheral auditory system is the fluid-filled cochlea of
the inner ear. The cochlea is the mechano-chemical transducer of the ear that initiates
neural responses.
However, from the viewpoint of acoustic transmission, the cochlea
simply serves as a load on the middle ear, acting to limit the movements of the ossicular
chain (Moller, 1965; Lynch et al. , 1982). At the oval window, where the stapes is
attached to the cochlea, the annular ligament holds the footplate of the stapes in place.
This ligament, together with the fluid inside the cochlea, serves as the main load of the
ossicles.
The anatomical description presented in this section applies to all mammalian ears,
Pars flaccida
ar
s
Pinna
Ear
Pars te
a) Coronal View
MalleL
Pars flaccid
Pars tensa
b) Inferior Lateral View of TM
Figure 1-2: Illustrations of a gerbil ear. a) Coronal view of a gerbil ear viewed caudally.
While it is not obvious in the figure, the middle-ear cavity of gerbil consists of several
chambers of complex geometry. These chambers are formed and incompletely separated
by several thin bony septa. Note that the two regions of the tympanic membrane reside
in different planes. b) View of tympanic membrane from the inferior-lateral aspect. The
geometrical differences between the pars flaccida and pars tensa are clearly visible. The
pars flaccida/pars tensa area ratio is approximately 0.11 (Kohlloffel, 1984). Drawings
from Ravicz (1990).
including our experimental subject -
the gerbil. Figure 1-2 shows coronal and inferior
lateral views of a gerbil car. Note that all structures discussed so far can be identified
in the figures. We also label the eggshell-like bony inferior wall of the middle-ear air
spaces as the bulla, a term generally used to describe the protruding middle ear cavity
wall observed in many mammals, such as gerbil, cat, chinchilla and guinea pig. Note the
large extant of the middle ear air spaces and bulla in gerbil (Figure 1-3); the acoustic
implication of such a hypertrophied bulla will be discussed in Chapters 3 and 4 along
with the experimental results.
PBIln
L~i
Ventral View
10 mm
Lateral View
Figure 1-3: Lateral and ventral views of gerbil skull. The hatched area indicates the
bulla. Note the relatively large size of the bulla with respect to the skull.
1.3
Modeling of acoustic systems
Before we proceed with a discussion of middle ear modeling, it would be beneficial
to briefly review the basics of acoustics, in particular the modeling of simple acoustic
elements in the low frequency region. The general study of acoustics concerns the understanding of sound, and to a more refined level, the vibrations of molecules. The physics
underlying the principles of sound and vibrations has been greatly advanced in the last
100 years by such investigators as Rayleigh, Stokes, Thomson, Helmholtz, Sabine and
others. The work of these pioneers provides us with a great mathematical repertoire
for the general analysis of acoustical and vibratory signals. The majority of these techniques are in the form of differential equations describing the physical phenomena of
vibrations, mostly in the form of general wave theory (Beranek, 1954; Fletcher, 1992).
These mathematical tools have been used in the acoustical analysis of many areas, such
as speaker and microphone designs, architectural acoustics, environmental noise control,
and in biological systems.
1.3.1
Low frequency circuit analogs
In cases where the system under study is small in dimension compared with the sound
wavelength 3 , we can greatly simplify acoustical analyses. In these cases, spatial variations of sound pressure and volume velocity4 in the system can be ignored, and we can
represent the whole structure as a lumped unit fully described by these two quantities.
For those familiar with electrical circuits, the acoustical structures can be defined as
circuit analogs, for which quantitative solutions can be obtained using well established
analytical techniques. As we will see, the first order mathematical relationships describing the acoustical properties (pressure p and volume velocity U) 5 of simple systems such
as tubes, small cavities, membranes, and small apertures are the same as the three passive
lumped elements commonly used in electrical circuits: inductor, capacitor, and resistor.
3
1n this case, small means that the dimension of the system is less than one-tenth of a wavelength.
Sound pressure and volume velocity are the two variables that fully describe the sound wave. Volume
velocity refers to the collective movements of a unit volume of medium molecules per second, and sound
pressure refers to the amount of alternating increase and decrease in atmospheric pressure as a result of
this motion. These two quantities are the preferred variables in acoustic circuits. When two acoustic
elements are interconnected, the volume velocity at the adjoining node is always conserved (analogous
to the conservation of electrical current at an electrical node). As a result of this analogy, acoustic
structures can be modeled as electrical circuits.
5
All acoustical variables used in this thesis are expressed in the complex frequency domain, and they
are printed in bold (e.g. p, U). In occasional instances where time domain analysis is needed, the
variables are italicized and their dependence on time are explicitly noted (e.g. p(t), U(t)). Details on
frequency analysis and complex variables can be found in most general circuit texts, such as Desoer and
Kuh (1969), Nilsson (1990).
4
]In1this paradigml, sound pressure is analogous to electrical voltage and sound volume
velocity is analogous to electrical current. Since most biological systems, including the
imamlmalian middle ear, consist of interconnected tubes, cavities, and membranes, we
(can solve the acoustical problem by simply observing the behaviors of the corresponding circuit analogs. This method has proven to be more convenient and insightful than
solving systems of simultaneous differential equations.
Since the sound pressure p and volume velocity U fully describe the sound wave in
a structure, it follows that the complex acoustic impedance Z = p/U fully describes the
characteristics of the structure itself. Equivalently, acoustic structure is often defined
in terms of its admittance Y = 1/Z = U/P. For a wide and short open tube with
radius r and length 1, the application of alternating pressure p(t) between its two ends
generates a force of p(t)wr 2 . This alternating force causes the air molecules in the tube
to accelerate back and forth like a simple mass. Since the enclosed air mass is pol,'r
2
(Po = 1.19kg/m3 is the density of air at standard temperature and pressure), it follows
from simple Newtonian physics that
Pol dU(t)
wr 2 dt
Taking the Fourier transform of Eqn. 1.1 yields
p = jwpPo'2 U
7rr
(1.2)
where j is the imaginary number V-1, w = 2wrf is radian frequency, and p and U are
the complex amplitudes of sound pressure and volume velocity. Comparing Eqn. 1.1
with the constitutive equation of an inductor:
dit
v(t) = L di(t)
(1.3)
shows that the wide open pipe behaves like an inductor, with inductance pol/rr2 , as
shown in Figure 1-4a. This information can also be obtained from Eqn. 1.2, where
the complex acoustic impedance Z = p/U can be found to be jwpol/rr2 , which is the
frequency domain representation of an inductance pol/rr2 .
If the cross sectional area of the pipe is small, its large internal surface provides significant friction to the movements of air molecules. In this case, the acoustic impedance
has a resistive component in addition to the inductance. In a resistive environment, the
force (or pressure) needed to displace a unit mass is directly proportional to the velocity
of particles:
(1.4)
p(t) = RAU(t)
where RA is the acoustic resistance of the structure. Generally RA is frequency-dependent
and is difficult to describe with a simple analytical equation. However, for small enough
apertures and with a low-viscosity fluid like air, we can approximate the resistance
(Fletcher, 1992):
, .2x
A
1
RA RA1.2
1.×x 0
S-(POC)Wl
rr
r ) 1/
•
2x
0 33
01/
r3
(1.5)
where c = 345m/sec is the propagation velocity of sound under normal atmospheric
conditions. For a tube of very small diameter (r < 0.002/vJ), the acoustic resistance
approaches an asymptote that is independent of frequency (Beranek, 1954). The complex
U
-
P1 .OU
C) iP
1
*
U
2V2
V1 AV
a) A wide, short open tube with
radius r and length I
U--
~
2
b) A very narrow tube with
radius r and length I
U
-*01
P1
*P2
V1
Vi .__V
2
c) An elastic membrane with
stiffness k
d) An enclosed cavity with
volume V
Figure 1-4: Circuit representations of lumped acoustic elements. In these four lumped
circuit analogs, pressures (P 1 and P 2 ) are represented by voltages (V 1 and V 2 ), while
volume velocity (U) is characterized as current (i). a) A wide, short open tube can
be modeled as an inductor, with inductance pol/7rr 2 . b) For a very narrow tube, the
impedance is dominated by the resistance (Eqn. 1.6). At higher frequency, the inductance
could become significant and must be included in the model. c) For a membrane with
average stiffness k and area A, the model capacitance (or compliance) is simply A/k. This
model is only valid for frequency range below the membrane's lowest resonance frequency.
Above that frequency, a series inductor and resistor must also be included. d) An enclosed
cavity can be modeled as a grounded capacitor. The capacitance (or compliance) of the
capacitor is inversely proportional to the volume of the cavity: CA = V/poc 2 .
acoustic impedance of such a tube is
ZA
8rYl
4
7rr 4
3
Pol2
7rr
(1-6)
(1.6)
where r is the viscosity coefficient, q = 1.86 x 0l-5 Nsec/m 2 at 20 0 C and 0.76mHg. Note
that even though the inductance of a very thin tube is 1.3 times bigger than a larger
diameter tube, its impedance is greatly dominated by the resistive component (due to
the contribution of 1/r 4 in the resistive term). Therefore, it is sufficiently accurate to
model a very thin tube as a simple resistor, as illustrated in Figure 1-4b.
Another simple acoustic element is a small enclosed cavity of volume V with a single
inlet. If the cavity is small compared to the wavelength of the applied pressure (i.e.
the applied ac pressure p(t) is uniform throughout the volume) and the motion of air
particles is small compared to the dimensions of the enclosed volume, then the adiabatic
law6 dictates that
poc
p(t) =
2
IJU(t)dt
(1.7)
or in frequency domain:
p =
U
(1.8)
jwV
Comparing Eqn. 1.7 with the constitutive equation of a capacitor:
v(t) =
ji(t)dt
(1.9)
clearly illustrates the capacitive (or compliance) behavior of an enclosed cavity. One
6
Adiabatic law applies to situation where heat transfer from the air medium to the cavity wall is
negligible. This condition holds true for sound waves in all but the very lowest audible frequency range.
important consideration in modeling a cavity as a capacitor is the topological position of
this two-terminal electrical device. Since the applied pressure p(t) is defined as the change
from equilibrium pressure (which is modeled as a ground node or voltage reference),
one of the capacitor terminals must always be at ground potential (Figure 1-4d). This
restriction thus eliminates the possibility of inserting a "cavity capacitor" in series with
other acoustic elements.
To achieve a series-capacitance configuration, it is necessary to utilize a stiffness controlled diaphragm or membrane (Figure 1-4c). However, besides the stiffness property,
all membranes possess to a varying degree certain mass like behavior due to the inertia
of their membranal fibers. As a result of the interactions between these two components,
all membranes resonate at certain preset frequencies. Only at frequencies lower than the
lowest resonance frequency can we model a membrane as a series capacitor. A more accurate and general representation of membrane consists of series capacitor, inductor, and
resistor -
the inductor accounts for the mass like property and the resistor represents
the damping and frictional losses due to the membranal movements.
1.3.2
High frequency representations of acoustic systems
The maximum linear dimension of the entire gerbil middle ear (the bulla cavities) is on
the order of 10mm. To model such a system with the low-frequency circuit analogs developed in the previous section would entail a frequency limit of approximately 3.5 kHz7 .
For frequencies significantly above 3.5 kHz, the pressure in the middle ear is no longer
uniform at any given time. As a result, a lumped quantity such as a voltage can no
7
In developing the lumped parameter system, we assume that the wavelength of the sound wave
is at least ten times larger than the dimension of the structure. In this case, the frequency limit is
Jf = c/A
3.5 kHz, assuming c = 345 m/sec is the propagation velocity of sound, and A = 0.1 m is ten
times the typical gerbil middle ear dimension.
longer accurately represent the spatially distributed pressure wave. Since the audible
range of gerbils extends beyond 20 kHz (Ryan, 1976), other modeling techniques will be
needed to cover the entire functional frequency range.
One general approach is to model the acoustic structures as systems of distributed
parameters. A straightforward implementation of such a system is to use the finite element modeling technique. Such implementation provides a large degree of freedom,
thus increasing the flexibility of modeling a complex system. However, such capability
is achieved at the expense of increasing computational cost and the loss of physical correlations between model parameters and acoustic structures. Fortunately, for structures
with well defined geometry, there exist special techniques that would provide accurate
high frequency modeling, while utilizing only a limited number of parameters. For instances, tubes and horns can be modeled as transmission lines, and membranes emulated
as shells. The mathematical constructions of such models can often be formulated in
terms of two-port networks. This two-port modeling technique is used in Section 3.1.1
to represent the bony ear canal of the gerbil.
1.4
Middle ear models
As pointed out in Section 1.1, there is no active element present in the middle ear;
therefore, it is justifiable to treat the middle ear in the framework of passive mechanoacoustical structures. Since the main focus of this thesis is on the effects of pars flaccida
in middle ear transmission, and the effects of the flaccida appear mainly in the low
frequency region8 , the acoustical structures can be accurately modeled as circuit analogs.
8
As will be shown in Chapter 3, the effect of pars flaccida is observed primary at frequencies below
2 kHz.
Figure 1-5 depicts the key structures and the relevant acoustical variables of the
gerbil middle ear.
As discussed on page 19, the gerbil tympanic membrane consists
of two regions of distinct physical characteristics.
As a result, application of sound
pressure in the ear canal, PEC, is likely to induce different vibratory patterns on the
pars flaccida and the pars tensa. To better describe this phenomenon, it is necessary to
represent the volume velocities of these two regions as two separate acoustic variables,
1UpF
and UpT. The sum of these two variables is UT, the volume velocity of the entire
tympanic membrane. The movement of the pars tensa causes the subsequent vibration
of the malleus, incus, and stapes. The ossicular bones, however, are not the only load on
the tympanic membrane. The movement of the pars flaccida and pars tensa must also
compresses the air in the bulla cavity, generating sound pressure in the middle-ear cavity,
PMEC. In this reasoning scheme, the volume velocity entering the middle-ear cavity
must necessarily be the same as the volume velocity of the tympanic membrane, UT, as
they all involve the displacement of the same membrane. This observation has important
implication in middle ear modeling, as it dictates a series configuration between the bulla
cavity and the tympanic membrane-ossicular complex. At the end of the ossicular chain,
the motion of the stapes produces volume velocity U s at the oval window, which serves
as the input to the inner ear.
Several quantitative models have been proposed to represent the acoustical behavior
of the middle ear. The simplest models share the simple network topology shown in
Figure 1-6. One central feature of this model is the presence of the series admittance
krCAV
representing the middle-ear cavity. The middle ear input impedance YT =
UT/PEC is thus the series combination of YCAV and the total admittance contribution
from tympanic membranes, ossicular bones, and cochlea, YTOC.
Middle-ear
-
air spaces
SCochlea
Os
-.Bulla shell
tensa
Figure 1-5: A schematic representation of the gerbil middle ear. The acoustic variables
used in middle ear modeling are shown circled in this diagram. PEC = sound pressure in
the external ear canal; UT = volume velocity of the ear canal (which equals the volume
velocity of the entire tympanic membrane); UPT = volume velocity of the pars tensa;
UpF = volume velocity of the pars flaccida; U s = volume velocity of the stapes - a
measure of the input to the inner ear; and PMEC = sound pressure in the bulla cavity.
PEC
ECB)
Figure 1-6: The simple middle ear series model. In this representation, all bulla cavities
are lumped as a one-port admittance, YCAV. The total input admittance of tympanic
membranes, ossicles, and cochlea are represented by a two-port input admittance YTOCThe loading effects of stapes and cochlea are modeled as a one-port, YSC, with US, the
volume velocity of the footplate, as its sole input. The other model variables are: PEC,
sound pressure at the ear canal; PMEC, sound pressure at the middle-ear cavity; and
UT, volume velocity of the tympanic membrane.
One important corollary of this series model is that all volume velocity entering the
middle ear cavities is used to compress the tympanic membrane and ossicles, and consequently contributes to the inner ear input. As described in Section 1.2, this assumption
may not be entirely accurate. The presence of pars flaccida (and to some lesser extent a
small uncoupled portion of pars tensa) may provide a potential shunt path for the sound
volume velocity entering the ear canal. As a result, the middle-ear model for animals
with significant pars flaccida needs to be revised to include its effect 9 .
The function of pars flaccida was first described by English surgeon Henry Jones
Shrapnell in 1832. He suggested that the compliance of parsflaccida is mainly responsible
for protecting the stiffer pars tensa from loud noises and large pressure fluctuations by
9
Zwislocki (1962), Moller (1965), and Kringlebotn (1988) all provided a shunt path in their model
for the uncoupled portion of the tympanic membrane. However, they made no provision for the physical
correlation of such a path to pars flaccida, nor did they quantify the effect of the shunt path on middle
ear acoustic transmission.
reducing the quasi-static pressure build up across the tympanic membrane. A similar
conclusion was reached by Stenfors et al.(1979). However, Hellstr6m et al.(1983) found
that in rats, which have one of the largest pars flaccida-parstensa ratio among mammals,
the volume involved in the pars flaccida movements is only 0.5 percent of the middle ear
volume, not significant enough to equilibrate the large changes in pressure that can occur
within the middle ear.
Thus far, no experimental studies have been done to investigate the role of pars
flaccida in sound transmission through the middle ear. As a result, the role of pars
flaccida in middle-ear mechanics is largely unknown; consequently it is often omitted
from most middle ear models. In a note published in 1984, KohllSffel proposed that
pars flaccida may act as a shunt route for acoustic volume velocity at the tympanic
membrane, thus reducing the power available to the inner ear. Such a middle ear model
is represented in Figure 1-7.
PEC
U'
Figure 1-7: Series model that includes the effect of pars flaccida. The pars flaccida
is represented as a one-port complex admittance acting across the input of the pars
tensa-ossicular complex. The variables of the model are: PEC, sound pressure at the
ear canal; PMEC, sound pressure in the middle-ear cavity; UT, volume velocity of the
tympanic membrane; UPT, volume velocity of the pars tensa; and UpF, volume velocity
of the pars flaccida.
In this model, the complex admittance of pars flaccida (YPF) is acting in parallel
with the input admittance of the pars tensa-ossicular-cochlear complex (YTOC). As a
result, if the input admittance of YTOC and YPF are in phase (e.g. both are compliance
dominated), then the addition of the pars flaccida could serve to reduce the flow of
acoustic volume velocity into the ossicular chain and the inner ear.
The four model blocks can be represented explicitly as circuit elements discussed in
Section 1.3 (Figure 1-8). The advantage of such a model is to allow direct quantification
of the auditory effect introduced by each modeled component, such as cavity compliance,
membrane damping, and ossicular mass. (1) The air spaces of the middle ear cavities
are lumped as a single capacitor.
This representation should be accurate in the low
Pars Tensa,
Malleus,& Incus
LIT
UPT f -------
----
PEC
P
Flai
U
I
I
U'
I
jiI1
U
Stapes &
Cochlea
I
YSc
sc
ddle
:ar
vities
CAV
][Figure 1-8: Low frequency circuit analog of the middle ear. This model represents the
compliance, mass and resistive properties of the middle ear as circuit elements discussed
in Section 1.3.
frequency region, where the acoustic effects of the foramina created by the middle ear
bony septa are negligible. Experimentally measured cavity admittance (see Chapter 3)
shows that this assumption is accurate up to 3 kHz. (2) The pars flaccida of the tym-
panic membrane is modeled as a series inductor, capacitor, and resistor as discussed on
page 27 to account for its compliance, mass-like and heat dissipative properties. (3) The
pars tensa, malleus, and incus are similarly modeled by an RLC circuit. In this case,
the addition of the malleus, incus, and their associated ligaments are assumed to add
additional mass, compliance, and damping to the tympanic membrane. Their effects can
therefore be lumped into the series inductor, capacitor, and resistor used to represent the
pars tensa1 o. An electrical transformer is added to this box to account for the impedance
transforming effect of the middle ear. This transformer takes into account the area ratio
between the tympanic membrane and the stapes footplate, the lever action of the middle
ear ossicles, and the buckling effect of the tympanic membrane. (4) The circuit analog
for stapes and cochlea admittance YSC follows the work of Lynch et al. (1982).
Ac-
cording to this report, YSC in cat is compliance dominated in the low frequency region,
mostly due to the stiffness of the annular ligament. As frequency increases, resistive
properties become significant; and at even higher frequencies, the mass-like properties of
the stapes and the inner ear fluid predominate. Similar results were obtained by Puria
et al. (1995) in human. The simplest circuit analog that is capable of achieving such
frequency dependent behavior is a simple series RLC circuit, as shown in Figure 1-8.
Most of the element values in this circuit representation, with the exception of pars
flaccida components, can be obtained by fitting the model to various measurement data
available in existing literature.
However, since no reported experiments were aimed
at studying the effect of pars flaccida in middle ear transmission, we have no way of
quantifying the flaccida's component values, and hence their impact on sound conduction.
10 We assume that the malleus and the incus are tightly coupled, such that there is no slippage in the
incudo-mallear joint. Therefore, no shunt branch is included to account for the loss of volume velocity
through such slippage.
Unge et al. (1991) reported that manipulation of the pars flaccida in the gerbil ear, in
an in vitro preparation, has no effect on the input admittance of the middle ear. In their
experiment, the pars flaccida was immobilized by either a) covering its external surface
with epoxy glue, b) covering the surface with elastic enamel in place of glue, or c) filling
the epitympanum with water, which covered the internal surface of the parsflaccida but
not the pars tensa. The tympanogram (essentially the input admittance) of the middle
ears was measured at 220 Hz and 660 Hz before and after the manipulations, and they
found little or no changes in their measurements. They consequently concluded that the
admittance of the gerbil middle ear is dominated by the pars tensa and the ossicles, with
very little contribution from the pars flaccida. Such a result is inconsistent with other
available experimental observations. Our preliminary data in rat and gerbil showed that
the middle-ear input impedance magnitude at low frequency (<1kHz) greatly increased
after the pars floccida was immobilized by dental acrylic, suggesting that pars flaccida
is either as compliant or more compliant than the pars tensa. This finding contradicts
the findings of Unge et al. (1991).
It is the purpose of this thesis to determine the relative importance of the pars
flaccida on the signal transmission properties of the middle ear, to test the validity of
the circuit model presented in Figure 1-8, and to measure the extent of its influence on
the eventual excitation of the cochlea. To accomplish these goals, the middle-ear input
impedance, bulla-cavity pressure, and round window cochlear potential are measured
under various middle ear conditions.
Several sets of experiments are conducted:
1)
with the pars flaccida and bulla wall intact; 2) with the pars flaccida intact, but the
bulla cavities widely opened; 3) with the pars flaccida replaced by a thin sheet of dental
acrylic -
thus greatly increasing its stiffness, and leaving the bulla wall intact; 4) with
the pars flaccida replaced by dental acrylic, and with the bulla cavities widely opened;
and finally 5) with the pars flaccida removed, but the bulla wall intact. The results
of these measurements are used to compute the pars flaccida parameters of the circuit
model, verify the linearity assumption in the model, and quantify the amount of inner
ear excitation which results from the acoustic properties of the pars flaccida.
Chapter 2
MIethods
2:.1
Experimental subjects
The anatomy of the gerbil middle ear has the attractive features of large cavities and
significant pars flaccida. These anatomical features make the manipulation of these
structures possible, thus allowing us to investigate their acoustic properties and their
effect on the animal's hearing. A total of twelve gerbils were used for acoustic and
electro-physiological measurements. Two out of the twelve gerbils were used to develop
the experimental methodology and to learn about gerbil anatomy. Descriptions of measurements made on these gerbils are documented in Appendix A.
2.2
2.2.1
Acoustic sources and their characteristics
Calibration theory
The configuration of the stimulus delivery system is shown schematically in Figure 2-1.
The acoustic source consists of an earphone for sound generation and a microphone for
sound measurement. The microphone readings are used as both an indication of sound
level in the ear canal and for the computation of middle ear input-admittance.
lnAntAl CAmpnt
Figure 2-1: Schematic drawing of the acoustic source in a gerbil ear. The acoustic source
assembly consists of an earphone (marked E in the diagram) and a microphone (M). The
source is coupled to the gerbil ear canal via a cemented brass ring.
The "Comparison Method" is used to retrieve admittance information from the pressure measurements. This method has been described in detail in the research literature
(Lynch, 1981; Rosowski et al. , 1984; Dear, 1987; Ravicz et al. , 1992; Lynch et al. ,
1994). Simply put, the sound source is modeled as a linear system, with its terminal
behaviors completely described by an equivalent volume velocity source US and internal
source admittance YS. This Norton-equivalent circuit model is shown diagrammatically
in Figure 2-2.
If U S and Ys are known, measurements of sound pressures generated
by the acoustic source in an unknown load, PL, can be used to compute the unknown
Source
Load
I
I
I
IUS
I
YS
I
+
I
I PL I
YL
II
I
I
II
LJ
..... I
L
I
I
Figure 2-2: Norton-equivalent model of an acoustic source with load. In this circuit
analog, the sound] source is represented by an ideal current source. The loading of the
internal admittance YS and load admittance YL determine the resulting pressure output
admittance:
YL
~ - YS
PL
(2.1)
The calibration process of the acoustic source thus includes the determination of the
complex amplitudes U
s
and YS. These two quantities can be obtained by measuring the
sound pressure produced by the acoustic source in two reference loads whose admittances
are known theoretically. From Eqn 2.1, it follows that
YS - PL1YL1 - PL2YL2
PL2 - PL1
(2.2)
where PL1 and PL2 are the pressures measured in the reference loads with known
admittances YL1 and YL2. US can then be calculated from Eqn 2.1 using either one
of the measurements.
In practice, we do not measure PL directly, rather, we measure the amplified voltage
output of the microphone, VL, which is directly proportional to PL:
VL = ksPL
(2.3)
where ks is a complex proportionality constant that includes the sensitivity of the microphone and the gain of the amplifier. It has units of volt/Pa.
Due to the proportionality relationship between VL and PL, substituting Eqn 2.3
into Eqn 2.2 allows us to cancel ks from the equation, and thus we have:
Y VL1YL1 - VL2YL2
(2.4)
VL2 - VL1
We cannot, however, eliminate ks from the expression of U S . As a result, a scaled
version of the source volume velocity is obtained:
ksUs = VL1(YS + YL)
= VL2(YS + YL2)
(2.5)
This is not a problem, however, as we are still able to compute the unknown load
admittance from ksUs, Ys, and VL:
Us
YL = U
PL
YS
ksUs
P
kSPL
YS
ksUs
V=
VL
YS
(2.6)
Since Eqn 2.6 is the actual equation used to determine the experimental input admittance, I will report the scaled volume velocity as the source volume velocity U s throughout this thesis. Us thus has the units of volt - m 3 /Pa - sec.
2.2.2
Source description and characteristics
Theoretically, the paradigm described in the previous section can be used to measure
admittance of any unknown load. In practice, the experimental inaccuracies of US, YS,
and PL limit the admittance and frequency range of our measurements.
One possible source of error can be explained in terms of the Norton-equivalent model
of the acoustic source. Judging from Figure 2-2, it is clear that if IYLI is significantly
smaller than the IYsi, the resulting pressure PL will be controlled primarily by the
internal source admittance, not the acoustic load. Thus, the resulting admittance measurements are highly dependent on the accuracy of IYs1, whereby a small experimental
error in source specification can result in erroneous admittance measurements. Consequently, if we can only specify IYsI with 10% accuracy, we will not be able to accurately
measures admittances which are smaller than 0.11Ys1.
The experimental uncertainty of the measured admittance is also directly dependent
on the uncertainty of the pressure measurements. We would therefore expect the strength
of the volume velocity source to be an important consideration in determining the signalto-noise ratio of the resulting sound pressure, and consequently the accuracy of the
measured admittance.
In order to produce reasonably accurate and consistent gerbil middle-ear inputimpedance measurements, two acoustic sources were used in our study. The combination
of these two sources enabled us to measure sound pressure and acoustic admittance over
approximately three decades of frequency and four decades of admittance magnitude.
Details concerning the construction of these two sources are described in Ravicz et al.
(1992)1. Briefly, one source uses a Knowles ED-1913 hearing aid receiver (Knowles Elec-
'A slight
modification has been made to the high frequency source, where the sound-delivery tube has
tronics, Elk Grove, IL) as an earphone and a Knowles EK-3027 microphone for sound
pressure measurement (Figure 2-3). The relatively small size of this source allows it to
C'-r A -rI f
'C-
KNOWLES ED-1913
HEARING-AID
EARPHONE
SURE
ASE
SOUND DELIVERY
TUBE
KNOWLES EK-3027
HEARING-AID
MICROPHONE
TUBE
PROBE-TUBE
DAMPER
SCR1
Figure 2-3: Cross-sectional diagram of the low frequency source. The sound delivery
tube is packed with cotton to decrease the internal admittance of the source. A small
tube is also inserted into this space to prevent static-pressure buildup in the source.
The screen is there to prevent fluids from entering the source and changing its internal
admittance.
have low admittance, especially at lower frequencies. This desirable feature is achieved
at the expense of lower source strength, particularly at frequencies above 3 kHz. Consequently, this source is used primarily for low frequency measurements, and will be termed
"low frequency source" or "lfs" in this thesis. The other acoustic source uses a Beyer
DT48 dynamic earphone (Beyerdynamic, Germany) as the sound source, while retaining
the same Knowles microphone (Figure 2-4).
This larger source has higher internal
been lengthened. This has some small effects on the source characteristics, as manifested in the slight
differences in U S and YS estimated in this study and Ravicz et al. (1992). The source construction
URE
KNOWLES EK-3C
HEARING-I
MICROPHOI
PROBE 1
SCREEN
Figure 2-4: Cross-sectional diagram of the high frequency source. This source is similar
to the low frequency source, but with the Beyer DT-48 earphone in place of the Knowles
ED-1913 receiver.
admittance than the ifs, especially at the lower frequencies. This limitation makes this
source unsuitable for measuring loads with low acoustic admittance. However, the Beyer
earphone is capable of generating larger sound volume velocity per unit driver voltage,
compensating for the shortcoming of the lfs. This source was therefore primarily used
for measuring acoustic loads with high admittances, in which large volume velocities are
needed to produce a good signal-to-noise ratio, as well as for high frequency measurements in all loads. This source will be referred to as "high frequency source" or "hfs" in
this thesis.
Figure 2-5 shows the internal input admittances and source volume velocities of the
high and low frequency sources, along with their 95% confidence intervals (which is
statistically equivalent to + 2 standard errors). The confidence intervals were calculated
from fourteen measurements made over a period of seven months. The consistency of the
source characteristics are evident from the tight error bounds shown in the figures. The
input admittance of the lfs shows compliant behavior over most of the frequency range,
resulting in low admittance at the low-frequency region. On the other hand, the source
admittance of the hfs is primarily resistive-dominated, with a small peak near 2 kHz, due
mostly to the resonance in the sound delivery tube. Note that at frequencies above 7 kHz,
the Ifs admittance increases dramatically. This is an intrinsic artifact of the ifs, a result of
cross-talks between the earphone and the microphone that do not depend on the actual
measured sound pressure level. This crosstalk phenomenon is clearly demonstrated in
Figure 2-6a, where the blocked microphone registered non-random baseline readings
that were independent of the real sound pressure levels. At frequencies above 7 kHz, this
artifact recording dominates the microphone output of the tygon tube measurement, thus
method, however, remains the same.
(a) Admittance
(b) Volume Velocity
C
* 10
U)
0
C-)
Ca
10
a)
S
10
0
0)
CO 90
a)
0)
0)
(D
CO,
ýC
CL-90
2
3
10
Frequency (Hz)
4
10
2
3
10
4
10
Frequency (Hz)
Figure 2-5: Internal admittances and normalized volume velocities of the acoustic
sources. (a) Internal admittance of acoustic sources. 14 measurements over a 7 month
period are used to calculate the 95% confidence intervals of these plots. The measurements include several pre and post-experiment calibration results. The error bounds are
small over most of the low frequency region. They increase slowly for both sources at
frequencies above 3 kHz, where the impedances are primarily resistive. These variations
are most likely due to the different conditions of cotton packing in the sound delivery
tubes, where the presence of fluid or other materials could affect their damping property.
The reference loads used to obtain the source admittances are described in Section 2.2.3.
(b) Normalized source volume velocities of the acoustic sources. The substantially higher
volume velocity output of the hfs shows the greater efficiency of the Beyer earphone as
compared to the Knowles earphone. Both sources exhibit bandpass behavior that could
decrease the accuracy of pressure and admittance measurements in the very low and
very high frequency region, especially in high admittance acoustic loads.
causing the gross inaccuracy in the admittance calculation. This phenomenon renders
the Ifs unusable at frequencies above 7 kHz. The volume velocity plots in Figure 2-5b
are normalized quantities. They represent the volume velocity outputs per unit driver
voltage 2 . The high frequency source shows approximately 20dB greater output than the
ifs, thus making it more suitable for measurements of high admittance acoustic loads.
In addition, the crosstalk artifact that plagued the lfs does not affect the hfs except at
frequencies above 10 kHz (see Figure 2-6b). Both sources show dramatic decrease in
volume velocity output at high frequencies. This could affect the signal-to-noise ratio
of measurements made in this region. The low frequency rolloffs are not as severe, but
they do pose a limitation for measurements at very low frequencies.
2.2.3
Acoustic loads for source calibration
Lynch et al. (1994) described the considerations involved in choosing suitable calibration
loads to minimize the experimental errors in determining U s and YS. The analysis
indicates that most error-magnifying conditions can be avoided if one of the reference
load admittances is larger, and the other is smaller than the source admittance:
IYLiI
<
lYsi
< IYL21
(2.7)
Two types of reference loads were designed to satisfy this requirement. A long Tygon
tube terminated by an acoustic resistor that matches the characteristic impedance of
the tube was used as the high admittance load, while a small stiffness-dominated cavity
2
The stimulus used in this study is a linear chirp rather than tone sweep, the voltage unit is therefore
not defined as the customary rms voltage. Instead, the amplitude of the uniform frequency spectrum
(which incidentally is equal to the amplitude of the chirp signal) is used as the reference unit. More
information on this topic is discussed in Section 2.4 concerning stimulus paradigms.
0
10
10-
o
0)
0-2
C
0. 10 -3
>
0
C,
-
10
-4
180
180
(D S90
Cno
ci1
0
C -90
180.
-180
10
2
10
Frequency (Hz)
10
10
2
10
10
Frequency (Hz)
Figure 2-6: Sound pressure recordings that illustrate the crosstalk artifact in the acoustic
sources. The pressure measurements were made with (a) low-frequency source and (b)
high-frequency source. Four pressure measurements are shown in this figure: two were
made in the 4 ul cavity and two were measured in the long Tygon tube. For one
measurement in each load, the microphone opening was completely blocked with clay.
The earphone driver voltage was set to either 0.1V (LFS) or 0.01V (HFS).
was used as its low admittance counterpart.
The accuracy of the source calibration
was verified by measuring acoustic admittances of other known reference loads using the
computed YS and US, and comparing them with their theoretical values. All reference
loads were designed such that their physical characteristics, including volumes, lengths,
and diameters, could be measured accurately for use in theoretical computations (Ravicz,
1990). Figure 2-7 illustrates how a reference load can be coupled to the acoustic source.
Table 2.1 lists the physical characteristics of all the reference loads used in this study,
Acoustic source
ce load
Clay
Figure 2-7: Coupling of reference load to the acoustic source. To ensure airtight sealing,
clay is used to fill the spaces between the contacting surfaces.
and Figure 2-8 shows the cross sectional diagrams of their physical constructions.
The reference loads were modeled according to the two-port transmission line equations proposed by Egolf (1977). This two-port model takes into account thermal losses
due to viscous friction and heat conduction through the cavity walls. The model uses
equations originally developed for application to transient fluid flow in pipes, and requires as input arguments the length, diameter, and the termination load of the cavity.
Figure 2-9 shows how the two-port model can be combined with the appropriate terminating conditions to model the reference loads. The computed load admittances are
shown in Figure 2-10.
Brass ring
Acrylic
a) 4gl cavity
Tvaon tube
c) Long tube
b) Brass cavities A,B,C,D,F
Knowles
d) Radiation tube 1,2
Brass
e) Acoustic resistor
Figure 2-8: Cross-sectional diagram of reference loads. All these reference loads contain
either a brass ring or washer that allows easy coupling to the acoustic source. a) The
4zl cavity, along with the long tube, are used to calibrate U s and YS. Its small volume
gives it the highest stiffness among all the acoustic loads. b) Brass cavities A, B, C,
D, and F all have the same constructions. The cavities are made of brass tubes with
a stainless steel dowel pin pressed in at one end. c) The long tube consists of a Tygon
tube inserted into a tapered brass tube to minimize any abrupt change in diameter. The
end of the tube is terminated by an acoustic resistor that matches the characteristic
impedance of the Tygon tube. d) The radiation tubes have the same construction as
the enclosed cavities except that the dowel pins are omitted. e) The acoustic resistor is
constructed by attaching a brass ring to one end of a radiation tube. The inner diameter
of the brass ring is approximately equal to the outer diameter of a Knowles acoustic
resistor, such that the Knowles resistor can fit snugly in the bored hole.
e------
Lossy
2-port
model
of a
rigidwalled
tube
Lossy
2-port
model
of a
rigidwalled
tube
0-
a) Mathematical model of all rigidly
terminated cavities
_ RC
b) Mathematical model of the
long Tygon tube
Radiation impedance
F
0-
0-
Lossy
2-port
model
of a
rigidwalled
tube
YRAl
MA
ICA
RA2
4
L
c) Mathematical model of radiation tube 1 and 2
M
Radiation impedance
-- - --MA
MA
L-
_j
d) Mathematical model of the acoustic resistor
Figure 2-9: Mathematical models of the acoustic loads. All acoustic cavities are modeled as lossy two-port transmission-line models, a) For all enclosed cavities, the rigid
termination is modeled as a load of infinite impedance (i.e. an open circuit). b) For
the long Tygon tube, the tube characteristic impedance Rc = poc/A is used as the
terminating impedance, where A is the cross-sectional area of the tube. c) The radiation tube is terminated by the radiation impedance, which was modeled after the circuit
2
analog by Beranek (1986). The circuit variables are defined as: RA1 = 0.1404poc/a
mks acoustic Q, RA2 = 0.318/a 2 poc mks acoustic 2, CA = 5.94a3 /poc 2 m5 /newton, and
MA = 0.27po/a kg/m 4 , where a is the inner radius of the tube. d) Both the spaces
in the Knowles resistor and the brass tube are modeled as transmission-line two-ports.
The radiation impedance is considered the load of the smaller Knowles cavity. The input impedance of this Knowles two-port, plus the Knowles resistance RA3 and Karal
inertance LK, act as the cascading load on the second two-port. RA3 = 100 mks MQ is
the specification of the Knowles resistor. The Karal correction factor LK (Karal, 1953)
is used to model the sudden change in cross-sectional area from the brass tube to the
Knowles cavity. Its value was determined from fitting experimental data to the model,
and was found to be 0.02 Henry.
Q))
Q
Qj)
10:
'o
4,
e
"-wud
Load
Diameter
(mm)
2.34
2.30
2.30
2.30
2.30
2.30
2.30
1.96
Length
(mm)
1.02
5.07
10.28
20.32
29.95
40.61
23.5
4.00
Volume
(Il)
4
21
43
84
125
170
-
Long tube
2.37
30 m
-
resistive
Radiation tube 1
Radiation tube 2
2.30
2.30
6.45
23.70
-
mass-like
mass-like
4 IL cavity
Cavity A
Cavity B
Cavity C
Cavity D
Cavity F
Acoustic resistor
Acoustic
characteristics
compliance
compliance
compliance
compliance
compliance
compliance
resistive
-
Table 2.1: Specifications of the reference loads. This table lists the dimensions and
primary acoustic characteristics of the reference loads used in this thesis. Note that
there are two spaces associated with the acoustic resistor (see Figure 2-8), thus two rows
are needed to specify its dimension. The characteristics of the larger brass tube is shown
on the first row, while the second row shows the dimensions of the Knowles acoustic
resistor inserted into the brass ring at the top of the load.
For the hfs, the source volume velocities and admittances (Figure 2-5) were obtained
using the 4 1l cavity and long Tygon tube as the calibration loads. Theoretically, these
two cavities can also be used to accurately calibrate the low-frequency source, as their
admittance magnitudes satisfy the constraint of Eqn. 2.7 (all these admittances are shown
in Figure 2-11). In practice, the low power output of the lfs and the high admittance of
the Tygon tube in low frequency regions caused the pressure response in the reference
load to be near the noise floor. Consequently, cavity F is used to calibrate the lfs for
frequencies below 900 Hz. At frequencies above 1500 Hz, the resonances of the cavity
F admittance adversely affected the accuracy of the calibration computation, thus the
long Tygon tube is used in this range instead. For frequency between 900 and 1500 Hz,
a linearly weighted average of the two measurements was used.
102
C
10
0
C-)
100
E
C)
.
10o
10-2
C,
Cz
-V
90
0
.- 10
-90
102
10 3
104
Frequency (Hz)
Figure 2-11: Admittances involved in the calibrations of acoustic sources. Consistent
with Eqn. 2.7, the admittance magnitudes of the high and low frequency sources are
intermediate to the admittances of the two reference loads: the long Tygon tube and the
41l cavity. To overcome the problem of lfs's low pressure output in the Tygon tube at
low frequency, cavity F is used at frequencies below 900 Hz.
2.2.4
Accuracy and limits of acoustic calibration
To verify the accuracy of the calibration results, admittance measurements in other
reference loads were made. Figure 2-12a shows the theoretical admittance of cavity D,
along with the measured results using the low frequency source. Consistent with the
discussions in the previous section, the Ifs measurement agrees well with the expected
value for frequencies up to approximately 6 kHz. Beyond that region, the high source
admittance and the low pressure output combine to cause the measurement to be grossly
inaccurate. The high frequency source measurement of cavity D admittance is shown in
Figure 2-12b. The accuracy of this source at high frequency is substantially improved,
while large errors are evident at frequencies below 200 Hz.
This verification process was performed on all the reference loads shown in Figure 2-8.
In order to determine the volume velocity limits of the acoustic sources, measurements
were repeated at various pressure levels. The errors 3 computed from these measurements were used to determine the range of impedance magnitude and frequency that
can be measured accurately. Appendix B contains the accuracy charts determined in
this fashion. The levels of the earphone driver voltage were varied over a 30 dB range:
from 0.32 V to 0.01 V for the Ifs (i.e. set the computer output to 1 V and varied the
attenuator setting from 10 dB to 40 dB), and from 0.032 V to 0.001 V for the hfs.
Results in Appendix B show that the usable range of the lfs was limited to frequencies
below 6 kHz for all voltage levels. This limitation on high frequency measurements was
the result of the low volume-velocity output of the earphone and the cross-talk artifact
between the earphone and the microphone. The low earphone output at the low frequency region also restricted the measurement accuracy, especially at admittance above
3
Error is defined as the difference between the measured and the theoretical values.
(a) LFS
10
(b) HFS
310
._10
U)
Co
00
Cl)
=0
C.)
•Vl10
0
-1
90
0
-90
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure 2-12: Comparison of theoretical and measured cavity admittance. (a) The Ifs
measurement result clearly shows that the ifs is more suitable for measurements at
frequencies lower than 5 kHz, as predicted from its source characteristics. (b) The hfs
produced substantially more accurate admittance measurements in the high frequency
region. Due to its large source admittance at low frequencies, significant errors can be
observed at frequencies below 200 Hz.
20 nS. Aside from these two regions, the Ifs showed great accuracy, with errors smaller
than 1 dB in magnitude and 50 in phase, over region that extend from 50 Hz to 6 kHz in
frequency and 0.1 nS to 20 nS in admittance (except when the driving voltage was set to
0.32 V). This measurement region encompasses the gerbil middle-ear input admittance
and middle-ear cavity admittance, as well as the internal admittances of both acoustic
sources. With the driving voltage set to 0.32 V, the generated sound pressures levels in
low admittance loads were beyond the measurable range of the microphone amplifier.
The clipped signals thus resulted in gross inaccuracy when measuring admittances below
0.5 nS.
The charts of the hfs show improved accuracy at frequencies up to approximately
10 kHz. No signal clipping occurred in any of the four voltage settings; thus, the accuracy
patterns were similar in all four cases. The lower limit of the measurable admittance was
restricted by the high internal admittance of the hfs (as discussed in Section 2.2.2). As
a result, the accuracy of the admittance measurements below 0.3 nS was substantially
inferior to that of the Ifs. The volume velocity output of the hfs earphone determined the
upper limit of the admittance measurements. With high admittance loads, the generated
sound pressure is reduced. This, along with the lower source output at low frequency,
caused the decrease in signal-to-noise ratio and increase in measurement errors in the
high-admittance, low-frequency region. At the high frequency end, the cross-talk artifact
was present only at frequencies above 10 kHz, making it more suitable for high frequency
measurements. Overall, the hfs provided accurate admittance measurements from 200 Hz
to 10 kHz in frequency, and from 0.3 nS to 200 nS in admittance amplitude.
2.2.5
Level dependency of source characteristics
The acoustic sources used in this study were assumed to be linear devices. This assumption required that source admittances and normalized source volume velocities measured
at different pressure levels be identical. To test the validity of this linearity assumption,
U s and YS were measured at several pressure levels. Figure 2-13 shows the admittances and the normalized volume velocities of the hfs obtained with the driver voltages
20 dB apart (the corresponding sound-pressure levels were approximately 70 dB SPL
and 90 dB SPL, respectively). Most physiological measurements were made within this
20 dB range. The results show that in both cases, the 95% confidence intervals have significant overlaps over all frequencies (measurements were also made at three intermediate
pressure levels between these two cases, and the results are similar). We can therefore
conclude that the linearity assumption is valid for the hfs, at least in the sound-pressure
range of interest.
The corresponding lfs measurements are plotted in Figure 2-14. Both U s and YS
show good consistency with very small error bounds.
However, the 95% confidence
intervals of the two YS show some small but noticeable differences for frequencies below 300 Hz. For US, the disagreements occur only at frequencies below 100 Hz. This
nonlinearity, while noticeable, is less than 2% over a 20 dB pressure range. This is significantly lower than the experimental uncertainty of most physiological measurements, and
therefore can be considered negligible. As a matter of consistency, all impedance measurements shown in this thesis were computed from the source characteristics obtained
at the same stimulus voltage level.
(a) Admittance
1
10
4)
Ul)
(9)
v
')
C)
-9 -90
.r-
10
3
Frequency (Hz)
103
Frequency (Hz)
Figure 2-13: Source admittance and volume velocity measurements of hfs at two pressure
levels. The two pressure levels were generated with the source driving voltages set to
1 and 10mV (The voltage values correspond to the amplitude of the chirp spectra).
The 95% confidence intervals are shown along with the means calculated for 14 different
measurements.
(b) Volume Velocity
(a) Admittance
C
.n10
O
0
C,)
E
a)
C-
1
0)
a)
0
0
-)
n -90
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
Figure 2-14: Source admittance and volume velocity measurements of Ifs
levels. The two pressure levels were generated with the source driving
10 and 100mV (The voltage values correspond to the amplitude of the
The 95% confidence intervals are shown along with the means calculated
measurements.
10
at two pressure
voltages set to
chirp spectra).
for 14 different
4
2.3
2.3.1
Acoustic calibration
Absolute calibration
Most measurements of interest in this thesis, such as middle-ear input admittances, earcanal-to-middle-ear pressure ratios, and middle-ear transfer functions, do not require
the knowledge of actual sound pressure levels in either the ear canal or the middle ear.
However, to ensure that the applied sound-pressure level was in the linear region of
middle-ear mechanics (Guinan and Peake, 1967; Nedzelnitsky, 1980), it was necessary to
determine the exact sound pressure level applied at the ear canal.
The absolute calibration of the sound sources required the use of a third microphone.
This reference microphone (a Larson Davis 1/4 inch microphone model 910B) was precalibrated with a Larson Davis piston phone that was known to generate 114 dB SPL
at 250 Hz. Since the reference microphone has a flat frequency response across the frequency range of interest, the piston phone measurement at a single frequency allowed us
to fully characterize the sensitivity of the reference microphone (in terms of
fllyrefI
to
P
).
Each sound source was coupled to the reference microphone in a small brass cavity.
The tonal stimulus generated by the earphone was then measured simultaneously with
both the sound source and the reference microphones.
Assuming that the pressure
measurements of the two microphones were the same 4 , their ratio allowed us to determine
the absolute calibration of the sound source for tonal stimulus:
Pa =
IVS
4
Pa IVrefl
IVref I IVs
(2.8)
(2.8)
Using the 1/10th wavelength criterion of Chapter 1, this assumption is valid at frequencies up 10 kHz
if the distance between the the two microphones is less than 3mm. Most of the calibration measurements
were made with the two microphones less than 1mm apart.
The calibration with the chirp stimulus required further computations. In SYSid (the
data acquisition software used in this study), the frequency spectra of chirp and tone are
scaled such that their spectral amplitudes are the same as the amplitudes of their time
domain counterparts. For example, a sine wave of unit amplitude and a linear chirp of
unit amplitude are both scaled by SYSID to have unit spectral amplitudes, even though
the spectrum of the sine wave has only a single component while the chirp spectrum
represents nfft/2 different sinusoidal components (nfft is the size of the discrete-time
spectrum). This convention is useful for the visual comparison of signal levels in both
time and frequency domains; however, it is mathematically incorrect. Since both the
chirp and the sine waves contain the same amount of power in the time domain, their
frequency spectra must also contain equal amount of power. The power of the chirp
spectrum (which is the square of the pressure amplitude) must therefore be rescaled by
a factor of 1/(nfft/2) to correct for this power discrepancy. if x is the amplitude of
the tonal spectrum, and y is the corrected amplitude of the chirp spectrum, the power
consideration thus requires that:
x
y=
(2.9)
(2.9)
vnfft/2
where 1/,/nfft/2 is the correction factor. With the tonal calibration factor determined
above, we can compute the new chirp calibration factor as:
Pa
IVsI
Pa
chirp
____
IVsI
1
tone
/nfft/2
(2.10)
-(2.10)
Multiplication of this calibration factor with the source microphone output V s thus
generates the sound pressure level in Pa.
2.3.2
Probe-tube microphone calibration
In the experiment, a probe-tube microphone was used to measure the gerbil middle-ear
pressure. The complex proportionality constant of the probe-tube microphone kpt was
most often different from that of the acoustic source ks (see Section 2.2.1). As a result,
we must determine the relationship between these two constants in order to meaningfully
compare the pressure levels in the ear canal and the middle ear cavity.
To calibrate their relative sensitivities, the acoustic source and the probe-tube microphones were coupled in a small cavity, such that the pressure measured by the two
microphones were considered equal. Consequently, the ratio of the two microphone output voltages was also the ratio of their proportionality constants:
Vs
ks
VpT
kpt
-
= m
(2.11)
where m is a new normalization constant. Figure 2-15 shows the experimentally obtained
m. The 95% confidence intervals were obtained from 14 measurements over a seven
month period.
When the probe-tube microphone is placed in the bulla cavity and the acoustic
source in the ear canal, the pressure ratio at these two locations can be obtained by
simply multiplying their voltage ratio with m:
VpT
VTm
VS
VpT
VpT kks8
V S kpt
PB
PB
PEC
(2.12)
where PB is the pressure in the bulla cavity, and PEC is the pressure in the ear canal.
101
E
C
CO
0
4-'
O
0CZ 10 0
._.
0
Z
180
C
CD
0)
a)
90
-~ 0
CD
CO,
-c -90
-180
10 2
10
10 4
Frequency (Hz)
Figure 2-15: The probe tube normalization constant m. Except at the lowest frequencies,
the normalization constant shows good consistency over the seven month measurement
period. The larger variations at frequencies below 100 Hz is most likely due to leakage
in some of the measurement setups. The peaks at 2 kHz are the results of resonance in
the source probe tubes. The difference between the high and low frequency sources will
be explained in Section 2.2
2.4
Stimulus paradigms
Two type of stimuli were employed in this study: chirp and tone sweep.
The chirp
stimulus was used to measure middle-ear input admittance, and ear canal and middleear pressures. The stimulus was synthesized digitally by performing an Inverse Fast
Fourier Transform (IFFT) of a flat frequency spectrum with quadratic phase (linear
group delay):
e~J{
.. l
::1411k=.0.
inc2
F~k]
ej -- T -
0
k = -_f_
2(2.13)
+ 1... - 1
where nfft = 2048 is the size of the discrete-time spectrum. The main advantage of using
a chirp signal was the speed of the measurement process. With the sampling rate of our
digital-to-analog converter set at 50 kHz, the duration of the whole stimuli was only
81.92 ms. This brief signal covers a frequency range from 25 Hz to 25 kHz. Each of our
measurements consisted of an average of 150 chirp responses, which took approximately
13 seconds to complete. This procedure saved a considerable amount of time compared
to a normal tone sweep. Depending on the frequency resolution of the measurement, the
tone sweep protocols require several minutes to complete. In fact, the time saved was
critical in achieving consistent measurements, as drying of the tympanic membrane and
physiological stresses placed on the animal can cause deterioration in both acoustic and
physiological measurements.
One major disadvantage of the chirp signal was the temporal spreading of signal energy. Since the signal had a linear group delay, the energy associated with a particular
frequency only occurred for a very brief period. This would not pose any problem if
a system was linear and the measurement noise was a strictly independent zero-mean
random process. Such requirements are sufficient to guarantee the convergence of the
mean asymptotically to its true value. This condition held true for our acoustic measurements that included middle-ear input admittance, ear canal, and middle-ear pressure. Thus, sufficient averaging of these responses could provide results of high accuracy.
Our electro-physiological measurements, however, did not satisfy this requirement. The
round-window cochlear potential was not entirely linear, and the electrical artifacts of
the electrode were neither independent nor a zero-mean random process. In fact, signals
that contain multiple frequency components presented simultaneously or closely following each other could trigger highly nonlinear cochlea responses (Pickles, 1988). As a
result, chirp signals were not suitable for cochlear potential measurements, and tonal
stimulation were used instead.
Our tone sweep measurements consisted of 50 logarithmically spaced continuous tones
over the range of 12 Hz to 10 kHz. In order to increase the signal-to-noise ratio of the
noisy cochlear potential measurements, each tone was presented 50 times, with a total
duration of 8.192 sec.
The average of these 50 responses was used to calculate the
magnitude and phase of the cochlear potential at that frequency. The entire tone sweep
protocols consumed approximately 7 minutes.
For both chirp and tonal stimulus, measurements were made at a minimum of two
different sound-pressure levels. For the lfs, measurements were usually done with the
driver voltage set at 10 or 100 mV (voltage level refers to the amplitude of the chirp
signal). For the hfs, driver voltage were set at 1 or 10 mV. Such voltage levels correspond
to approximately 50-80 dB SPL sound-pressure level, well within the linear range of the
gerbil middle ear.
2.5
Experimental configuration and procedures
Figure 2-16 shows the overall schematic diagram of the experimental setup. A computer
based data acquisition system is used to control the measurement process. The following
sections will describe the methods used in this study in detail.
2.5.1
Animal preparation
All gerbils were anesthetized with sodium pentobarbital (Nembutal) at 70 mg/kg of
body weight. The body temperature was monitored throughout the experiment and
maintained between 34 and 370 C with a heating pad. The paw pinch reflex was checked
periodically during the procedure, and supplemental doses of Nembutal were administered as required. To prevent excessive secretion, Atropine at 1mg/kg of body weight
was administered every two hours.
The pinna of one ear (usually the left) was removed and the ear-canal excised as
necessary to allow the acoustic source to be placed against the external auditory canal.
A small metal ring was cemented to the skull around the ear canal opening to allow rapid
and repeatable removal and replacement of the acoustic source. The ring also served to
facilitate an airtight seal between the source and the skull. Since there is evidence that
anesthesia interferes with Eustachian-tube function (Guinan and Peake, 1967; Hutchings,
1987), the gerbil middle ear was vented by sealing a long thin tube to the surface of the
bulla (100 mm long and 0.25 mm inner diameter). Due to the small size of the tube, it
was able to prevent static pressure build up in the bulla cavity, while still acting as an
acoustic open circuit 5 . The animal head was held in position by hooking the jaw around
5
The cutoff frequency of the vent tube was determined to be approximately 70 Hz. It was computed
using the modeling techniques described in Chapter 1. Specifically, the bulla cavity (V = 220l/) was
2
modeled as a capacitor (C = V/pc ), and the vent tube was modeled as a series inductor and resistor
AT&T Personal
Computer
microphone
Gerbil Ear
Figure 2-16: Schematic diagram of the experimental setup. An AT&T personal computer
with a DSP-16 data acquisition board was used as the controller of the experimental
measurements. The computer generated signal was delivered to the earphone via an
attenuator and a power amplifier. The resulting acoustic and cochlear potential responses
were acquired by the computer after the signals were amplified.
a vertical rod. Pressure measurements were made with the animal lying on its side and
the experimental ear up. These procedures have been reviewed and approved by the
MIT Committee on Animal Care-Protocol #92-003.
2.5.2
Instrumentation
The instrumentation involved in the experiments is schematically shown in Figure 2-16.
A DSP-16+ data acquisition board from Ariel (Highland Park, NJ), with its on-board
TMS32020/C25 DSP processor, was placed in an AT&T 486 personal computer. The
DSP-16+ board had two channels of 16-bits analog-to-digital (A/D) and digital-to-analog
(D/A) conversions for stimulus generation and data acquisition. In our experiments, only
one channel of D/A and two channels of A/D were used. SYSid (an acronym for System
Identification), an audio-band test and measurement system from Ariel, was used as the
software for controlling the experiments.
The digitally synthesized stimulus (either chirp or tone) was converted by the D/A
converter into analog signals according to the sampling rate and amplitude specified by
SYSid. The signal was passed through an anti-aliasing filter and an adjustable attenuator
to set the signal level. The resulting output was used to drive the earphone of the
acoustic source through a Crown D-75 Power Amplifier set to unity voltage gain. The
power amplifier was there to provide the necessary current to drive the earphone, as
well as to effectively increase the input impedance of the earphone in order to prevent
unwanted loading attenuation of the signal.
There were three recordable responses in the experiment: the ear-canal sound pressure, the middle-ear sound pressure, and the round-window cochlear potential. Since
(Eqn. 1.6). The cutoff frequency was then determined as the parallel resonance frequency of these two
acoustic elements.
only two input channels were available, only two responses were measured simultaneously. As shown in Figure 2-16, the output from the ear-canal microphone is always
connected to channel A of the DSP-16+ A/D converter. The second input channel was
then used to record either from the round-window electrode or middle-ear probe tube
microphone. All the input signals were amplified by Grass P511K amplifiers before be6
ing quantized by the data acquisition system. The two measured transfer functions
were stored by the computer in the form of time domain impulse responses for further
analysis.
2.5.3
Cochlear potential measurements
One important assumption made in the middle-ear models presented in Chapter 1 is that
input to the inner ear is strictly dependent on the pressure across the tympanic membrane. To uphold this assumption, it is necessary for the pressure difference to produce
a proportional vibration velocity at the malleus, which in turn produces a proportional
vibration in the cochlear fluid, the principle transduction mechanism of the inner ear.
Over a limited frequency region, the cochlear potential near the round window is essentially a direct replica of the cochlear fluid vibration (Moller, 1963; Moller, 1965).
Figure 2-17 shows the data obtained by Moller (1965), which show the proportionality
relationship between the middle ear input impedance (inverse of admittance) and the
inverse cochlear potential at constant sound-pressure level at the tympanic membrane.
In our experiments, we will measure changes in cochlear potential, middle-ear input
admittance, and pressure difference across the tympanic membrane while manipulating
pars flaccida. Comparisons of these data will provide a direct indication of how the
6
Transfer function is defined as the ratio of the response to the stimulus.
25.00
I
I
I
I
I
I I
..... ....
...
..
-
20.00
-
Acoustic Impedanc
Cochlear Potential
rn
J
I
.00U
........... ............
- 4.......
.................... -------------------.......................
................ ----------- ---------- ---------
10.00-
I
I
..............I.......
I
.
.
.
.-
I
.
r-
1000
Frequency (Hz)
Figure 2-17: Cochlear potential and impedance measurements obtained from Moller
Plots show the proportionality relationship between the middle-ear input
(1965).
impedance and inverse cochlear potential at constant sound pressure level at the eardrum
in an anesthetized cat. Measurements were made with bulla intact. Impedance given in
logarithmic measure relative to 100 cgs units. CP reference is arbitrary.
acoustic transmission through the middle ear is affected by the condition of the pars
flaccida, and whether these effects can be explained by changes in either the input
admittance or the middle-ear sound pressure level.
2.5.4
Experimental protocol
A series of experiments were performed to answer questions concerning the role of pars
flaccida on the middle-ear pressure transmission, as well as to validate and quantify the
circuit models presented in Chapter 1. To accomplish these goals, the middle-ear input
impedance, ear canal and bulla-cavity pressures, and cochlear potential of gerbils were
measured under various middle ear conditions.
As illustrated in Figure 2-16, calibrated microphone-and-sound-source assemblies
were coupled to the ear canal through the cemented metal ring.
A round-window
electrode and a probe-tube microphone were placed in the bulla cavity through sealed
bulla holes. The middle-ear input admittance, YT, the cochlear potential, CP, and the
middle-ear cavity pressure, PMEC, were measured.
Several sets of experiments were
conducted: 1) with the pars flaccida and bulla wall intact; 2) with the pars flaccida
intact, but the bulla cavities widely opened; 3) with the pars flaccida replaced by a thin
sheet of dental acrylic (thus greatly increasing its stiffness), and leaving the bulla wall
intact; 4) with the pars flaccida replaced by dental acrylic, and with the bulla cavities
widely opened; and finally 5) with the pars flaccida removed, but the bulla wall intact.
In all cases where the bulla wall was unopened, the bulla cavity was vented by a long
thin tube, as explained in Section 2.5.1.
The different middle ear manipulations specified above are represented as switches
in Figure 2-18. When the pars flaccida is rigidified by dental acrylic, its impedance is
YTOC = UpT/(PEC-PB)
YT = UT/PEC
II
LIn-T
PEC
HOLE
'HOLE
Figure 2-18: Schematic diagram showing the effects of experimental manipulations on
the middle ear input admittance YT. YT is defined as the ratio of UT and PEC.
which in the natural state is the parallel combination of YPF and YTOC (YTOC is
defined as the input admittance of the pars tensa and its load) in series with YCAV.
The manipulations on pars flaccida is modeled as a switchable impedance with three
possible settings. When the parsflaccida is intact, the switch is in position "A", where
YPF acts as a shunt path across the pars tensa-ossicular complex. Switch position "B"
models the immobilized pars flaccida, which causes all the tympanic-membrane volume
velocity UT to pass through pars tensa. Switch position "C" represents a removed pars
flaccida, where it effectively shorts out the rest of the YTOC. The second switch models
the state of the middle ear cavities. Switch position "1" represents sealed middle ear
cavities (with the exception of the thin vent tube); widely opening the cavity wall is
represented as switch position "2", where YCAV is assumed to be short circuited; and
position "3" represents the configuration where the probe-tube hole on the bulla wall is
left open.
significantly increased due to the added stiffness. Since this impedance is in parallel with
YTOC (which has substantially higher admittance than the rigid acrylic), the parallel
combination is thus dominated by YTOC, and the first switch should therefore be set at
position "B". If at the same time, the middle ear cavity is widely open (second switch at
position "2"), the measured input admittance(UT/PEC) was essentially YTOC. To experimentally measure YCAV, the pars flaccida was removed, and the middle ear cavities
remained sealed (this correspond to the switches at positions "C" and "1" respectively).
At low frequencies, YCAV can be compared with the theoretical values, which can be
obtained through volumetric measurement of the middle ear cavity VCAV:
YCAV = jWVCA
poc2
(2.14)
After YCAV and YTOC are determined, the admittance of the pars flaccida, YpF,
can be found through the input admittance measurements of the undisturbed ear, YTThe spectrum of YPF can then be used to synthesize a circuit model of the pars flaccida
admittance. The resulting model admittance, YPF, can be tested against the input
impedance measured in other middle ear configurations.
Chapter 3
Experimental results
3.1
Middle-ear input admittance
Measurements of middle-ear input admittance were made in fifteen healthy ears from ten
gerbils. In six of these ears, measurements were made with both high and low frequency
sources. The lfs results were used to compute the input admittances below 3500 Hz; while
the hfs results were used for frequencies above 6000 Hz. Between these frequencies, a
linearly weighted average of both admittances was used to describe the results.
The accuracy of all admittance measurements was determined from the appropriate
source accuracy charts in appendix B. Only admittances that are accurate to within
2 dB in magnitude and 100 in phase are shown in this thesis.
Consequently, most
measurements made with the lfs alone were limited to frequencies below 6 kHz; while no
hfs measurements below 200 Hz were accepted. Measurements made with both sources
had a frequency range of 50 Hz to 10 kHz.
As explained in Chapter 2, chirp stimuli were used for all impedance measurements.
For the low frequency source, the earphone driver voltage was set to either 100 mV or
32 mnV (correspond to -20 dB and -30 dB re 1V), while the high frequency source was
generally driven by 10 mV or 3.2 mV chirp signal (correspond to -40 dB and -50 dB re
1V). The actual sound pressure levels generated by these stimuli were measured using
the calibrated probe-tube microphone and are shown in Figure 3-1.
180
CO
0)
90
W go
90
-90
-C
-180
2
10
3
4
Frequency (Hz)
Figure 3-1: The actual sound pressure levels generated by chirp stimuli in a gerbil ear
canal (B8). The sound pressure levels were computed from microphone outputs using
the calibration scheme described in Section 2.3.1. The amplitudes of the earphone driver
voltage are shown in the legend.
3.1.1
Correction for ear canal volume
The irregular geometry of the gerbil ear canal did not allow the microphone to be placed
directly on top of the tympanic membrane-the ideal anatomical position for measuring
middle-ear input admittance (see Figures 1-2 and 2-1). The actual pressure measurements in our experiments were made with the sound source coupled to the lateral opening
of the bony ear canal, leaving a small ear-canal cavity between the measuring microphone
and the tympanic membrane. Table 3.1 lists the volumetric measurements of this earcanal cavity made in fourteen ears from nine gerbils. The mean volume was found to be
18.6 pl, close to the published data of Schmiedt and Zwislocki, 1977 (20 pl) and Ravicz
et al., 1992 (21 pl).
Animal
B2
B3
B4
B5
B5
B7
B7
B8
B8
B9
B9
BO10
B10
Bl1
Ear
Left
Left
Left
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Weight
Ear-canal volume
(grams)
(ml)
59
51
53
65
65
66
66
57
57
54
54
60
60
59
17
17
18
18
19
17
23
20
19
18
19
18
17
21
Table 3.1: Body weight and ear-canal volume measurements of gerbils used in this study.
Two methods are available to remove the effects of the ear-canal cavity on the measured middle-ear input admittance. In the low frequency region, ear canal can be modeled
as a capacitor in parallel with the middle-ear input impedance, such that the theoretical
contribution of the canal can be subtracted from the overall measured admittance. At
higher frequencies, where the sound wavelengths are less than ten times the cavity dimension, distributed parameter models should be used instead. A commonly employed
distributed system models the ear canal cavity as a cylindrical tube represented by
transmission-line equations (Lynch et al. , 1994). Such a model can be further enhanced
to include the effects of viscous and thermal losses, and can be fully described in terms
of a two-port system (Egolf, 1977; Zuercher et al. , 1988; Ravicz, 1990; Ravicz et al. ,
1992). The two-port parameters are computed using Bessel functions of the zero and
the first kind, with the length and the radius of the cavity as the input arguments. The
two-port parameters used in this thesis were calculated with the dimensions of 2.4 mm
diameter and 4.1 mm length, consistent with our measured volume of 18.6 Al and the
measurements made by Ravicz, 1990.
Figure 3-2 compares the measured and the corrected middle-ear input admittances of
gerbil B8. The admittances calculated from both the distributed two-port model and the
lumped parameter circuit model are shown in the figure. The magnitudes and the angles
of the two corrected admittances are virtually identical from 50 Hz to 1 kHz. Major
discrepancies occur only for frequencies above 3 kHz, where they differ by as much as
60% in magnitude and 300 in phase at 10 kHz. While all discussions in this thesis will be
made in terms of low frequency circuit analogs, most admittance plots will be presented
at frequencies up to 10 kHz; the circuit analog was thus determined to be an insufficient
model for the residual ear-canal volume, and the distributed two-port model was used
instead. All input admittance measurements presented in this thesis were corrected for
the ear canal using the two-port method.
(I)
C:
C/)
03
0
010
E
CZ
0
100
90
,90
C)
0)
a)
_0
0
C)
CZ
00
-90
10
2
10
3
10 4
Frequency (Hz)
Figure 3-2: Measured and corrected gerbil middle-ear input admittances. The result of
the two-port ear-canal cavity correction is compared with the correction made by the
simple lumped circuit model. The two models agree in both magnitude and phase at
frequencies below 1 kHz. At higher frequencies, both their magnitudes and phases show
significant deviations.
3.1.2
General features of the measured middle-ear input admittance
Input admittance of intact middle ears
Measurements of the input admittance with the middle ear intact (but vented by a long
thin tube) were made in eight ears (Al, A2, B1, B2, B3, B5, B8, B9), and are plotted in
Figure 3-3. These measurements are denoted as Y' throughout this thesis. At frequencies below 2 kHz, the admittance is clearly compliance dominated, with the admittance
magnitude directly proportional to frequency for the most part, and the phase close to
900 (i.e. YI,
jwC', where C' is the series combination of the compliances of tympanic
membrane-ossicular-cochlear complex and bulla cavity). In this region, the measured
admittances are very consistent, with the maximum variation on the order of 5 dB in
magnitude -
an indication of the intersubject stability of C'. Measurements in five out
of the eight ears (Al, B1, B2, B8, B9) show a small but well defined resonance peak and
angle change in the 400-700 Hz region. The compliance below this resonance frequency
tends to be higher than the compliance above the resonance frequency. As we shall see
in the following sections, such behavior is consistent with our series model presented in
Chapter 1 (Figure 1-7 and 1-8), where the compliance and mass-like properties of the
pars flaccida interact to produce such a resonance peak. With the exception of ears
A1, B1 and B9, the admittances above 2 kHz are mostly resistance dominated, where
the magnitudes are approximately constant (between 6 and 20 nS), and the angles vary
between +450.
Some of the measured admittances deviate from the general characteristics described
above. The admittance angles of ears Al and B5 (which were measured with the hfs) at
frequencies below 400 Hz and the angle of B5 at approximately 6.5 kHz are all greater
than 900.
Such results must be in error, since it implies that the middle-ear input
80
10
CD
C-)
U)
O
01
0o
10 •
o
E
<(
ai) 1
C
-9
<D 10900
UO
(D
0)
Ca
CO)
-90
102
10 3
10 4
Frequency (Hz)
Figure 3-3: Input admittance of eight intact gerbil middle ears, Y'. Among the eight
ears, three (A2, B8, B9) were measured with both high and low frequency sources; these
admittance measurements cover a frequency range of 50 Hz to 10 kHz. Ears Al and B5
were measured with the hfs alone, thus their accuracy range was limited to frequencies
above 200 Hz. The three remaining ears (B1, B2, B3) were measured by the lfs alone,
which limited their measurements to frequencies below 6 kHz.
admittance contains negative real parts, thus making the middle ear a source of acoustic
energy. For ears Al, B1, and B9, the admittance magnitudes at frequencies above 2 kHz
feature several peaks and reversals in slope that are accompanied by angles significantly
less than -30'.
These admittance values suggest that these ears contain significant
mass-like components at high frequencies.
Input admittance with the bulla hole open
Figure 3-4 shows the middle-ear input admittance measured in the same ears as the previous section, but with the probe-tube hole on the bulla wall left open. These admittance
measurements are denoted as yHO in this thesis. Opening the bulla hole has two major
effects on the middle-ear input admittance. First, the resistive and mass-like properties
of the aperture form a parallel resonance with the compliance of the middle-ear cavity,
which is manifested as a sharp valley near 3 kHz on the input admittance plot. The
frequency of this resonance behavior can be predicted solely based on the volume of the
middle-ear cavity and the size and length of the bulla hole'. Below 3 kHz, the acoustic property of this parallel combination is dominated by the hole inductance, which
effectively "shorts out" the admittance of the middle-ear cavity. Consequently, the lowfrequency middle-ear input admittance (i.e. f < 1 kHz) is predominantly determined
by the compliance of the pars flaccida and the pars tensa-ossicular-cochlear complex.
These two effects are clearly visible in the middle-ear input admittance plots in Fig'The interaction between the bulla hole and the middle-ear cavity can be modeled as a parallel
resonance between the compliance (capacitance) of the cavity with the damping (resistance) and masslike property (inductance) of the bulla hole. These three quantities can be fully specified in terms
of the middle-ear cavity volume, VMEC, bulla-hole radius, r, and bulla-hole length (the thickness of
the skull), 1. The resistance can be obtained from Eqn. 1.4 and the capacitance from Eqn. 1.8. The
inductance can be computed by modifying Eqn. 1.2 to take into account the radiation effect of the
2
. With the cavity volume of 218 p1 (Lay, 1972), the measured hole radius
aperture: L = po(l+ 1.75r)/rTr
of 0.5 mm and thickness of 0.3 mm, the predicted resonance frequency is approximately 3 kHz.
U)O
O
C/
1
0
10
0
CO
11-.
E
a)
E
100
90
c(
a)
V
0
()
c.-
0~
-90
10
2
10
10
4
Frequency (Hz)
Figure 3-4: Input admittance of eight gerbil middle ears - with the bulla hole left
opened, yHO. The admittance measurements were made in the same ears, and using
the same sound sources as in Figure 3-3. The resonance caused by the open hole is
clearly visible in this figure.
83
ure 3-4. Consistent with theoretical consideration, the resonance peaks can be observed
at approximately 3 kHz. The lower resonance frequency observed in ear Al may be
the result of a partially covered bulla hole 2 , presumably by the leftover vaseline initially
used to cover the hole in the middle ear intact case. In the low frequency region, all
measured ears show higher admittances with the hole open than in the intact middle
ear, with the amount of increases ranging from 5 to 11 dB. Such results agree with our
expectation that opening the bulla hole eliminates the series compliance of the middleear cavity, thus increasing the overall input admittance. Without the cavity admittance,
the remaining low-frequency compliances show increased intersubject variation, where
the compliance values vary by as much as 10 dB. As will be discussed in the next few
sections, these compliance values are mainly determined by the acoustic properties of
the pars flaccida, and are greatly influenced by its physical condition. Another apparent
difference between Figure 3-4 and 3-3 is the increased prominence of the resonances in
the 300-700 Hz frequency range. This feature is another result of the removal of the
stiffer middle-ear cavity, allowing the pars flaccida compliance and mass to dominate
the low-frequency admittance measurements. At frequencies above 4 kHz, the hole-open
input admittance is very similar to the admittance of the intact middle ear.
3.1.3
Effects of membranal drying on middle-ear input admittance
In several earlier experiments, we tested the consistency of the measured input admittance by repeating the same acoustic measurements over a 2-3 hour period. The results
show good consistency for frequencies above 1 kHz, but they also reveal a systematically
varying trend at lower frequencies.
2
Figure 3-5a shows three middle-ear input admit-
The smaller the hole, the higher the inductance, and consequently the lower the resonance frequency.
tances measured over a two-hour period. As time progressed, the compliance-dominated
low-frequency admittance was observed to shift gradually to the right (higher frequency),
while the resonance near the 500 Hlz region was increasingly damped. The increase in
stiffness and resistance were found to be mainly a result of the drying of tympanic membrane, especially in the pars flaccida region3 . Figure 3-5b shows that the increase in
stiffness can be reversed by moistening the tympanic membrane on the lateral surface
using 0.9% saline solution. After rehydration, however, the input admittance remained
unstable, as additional drying continued to increase the membranal stiffness. The lowfrequency stiffness was reverted to its original values approximately 1 hour after the TM
was moistened. The reduction in damping was not restored by the simple rehydration
process.
To overcome the complication of this drying effect, our experimental protocol was
revised to shorten the measurement duration as much as possible. For each gerbil ear,
measurements were made in only one middle-ear configuration (either with the middle
ear opened widely or the middle ear intact). This change shortened the initial acoustic
and cochlear potential measurement time (when the TM was undisturbed) to 15 to 30
minutes, during which the tympanic membrane was repeatedly moistened. The pars
flaccida was then stiffened, obviating the need for further moistening. This protocol was
used in animal B8, B9, BO10, and Bl1, and the resulting measurements were found to be
more consistent than the earlier experiments. Measurements obtained from these four
animals will be emphasized in this chapter, while the results obtained from the earlier
experiments are included in Appendix C.
3
The admittance region that varied the most is dominated by pars flaccida. See the next Section for
experimental evidence that support this conjecture.
(a)
(b)
C:
CO
O
0
0a
C10
E
CO
E
90
10 o
VCI)90
r- -90
IL
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure 3-5: Effects of membranal drying and moistening on the gerbil middle-ear input
admittance, yHO. (a) The input admittances of a gerbil middle ear (gerbil A2) with an
open bulla hole were measured over a two hour period. The shift in the low frequency
admittances and the reduction of resonance amplitudes around 500 Hz are clearly visible
in these plots. (b) The input admittances of a gerbil middle ear (gerbil B2) with an
open bulla hole were measured before and after the tympanic membrane was moistened
by 0.9% saline solution. The low frequency compliance was increased by the rehydration process. Approximately one hour after the TM was moistened, the low frequency
admittance shifted back to the original level, presumably due to additional drying of the
tympanic membrane.
3.1.4
Input admittance before and after manipulation of pars flaccida
- ears with intact bulla
Measurements of input impedance of the intact middle ear were made in the left ear of
five gerbils (Al, A2, B1, B2, B3) and the right ear of three gerbils (B5, B8, B9). In
this configuration, a long thin vent tube was also inserted into the middle-ear cavity to
prevent the buildup of static pressure. Of these eight ears, only measurements made in
A2, B8, and B9 included manipulation of the pars flaccida, where it was either stiffened
or removed. Figures 3-6 shows the input admittance measurements made in gerbils B8
and B9. Three admittance plots are displayed in each figure, one was measured with
the tympanic membrane intact and undisturbed (Y'), another one with the parsflaccida
stiffened by dental acrylic (YIs)4 , and a third one with the parsflaccida removed (YIR)
A quick examination of these three admittance plots allows us to determine three
important parameters of our middle-ear model shown in Figures 1-7 and 1-8: the compliance of the middle-ear cavity (CCAV), the compliance of the parsflaccida (CpF), and
the compliance of the pars tensa-ossicular-cochlear complex (CToc). With the pars flaccida removed, the middle-ear input admittance is for the most part the admittance of
the middle-ear cavity - which is primarily compliance dominated, especially in the low
frequency region. Measurement of this acoustic compliance can thus be used to compute
the middle-ear cavity volume. This cavity compliance, CCAV, can be calculated directly
4The
notational convention used in this thesis is to indicate the condition of the middle ear in the
superscript of the admittance variable (e.g. I for intact), and to represent the manipulation to the pars
flaccida in the subscript of the variable (e.g. FS for pars flaccida stiffened).
(a) Gerbil B8
(b) Gerbil B9
(0 2
C)
Q
4-"
CI
u)
0
E
W
W.0
"0
T
0
C-O
-C -90
0.
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
Figure 3-6: The middle-ear input admittance measured in the right ears of gerbils B8
and B9-middle ear intact. Three measurements are shown in this figure: 1) with a
normal and undisturbed tympanic membrane, Y ' , 2) with the pars flaccida stiffened,
flaccida removed, Y1F R . The alphanumeric characters (which
Yp
FS' and 3) with the pars
are enclosed in parenthesis) following each legend indicate the switch positions used to
represent the particular experimental manipulations (see Figure 2-18).
from the low-frequency admittance magnitude plotS:
FR
CCAV
(3.1)
27rf
With the mean compliance of 1.67 x 10- 3 mm 3 /Pa, the measured values correspond to
an effective middle-ear volume of 230 pl, similar to the middle-ear air volume measured
by Lay, 1977 (218 jl).
When the pars flaccida and middle-ear cavity are intact, the admittance of the right
ears of B8 and B9 show all the features described in section 3.1.2. When the parsflaccida
is stiffened with dental acrylic, the high-frequency input admittance Y
is similar to
the admittance measured in the normal ear, while the low-frequency admittance is significantly different. These differences provide a means of determining the effects of pars
flaccida on the middle-ear input admittance. The dental acrylic increases the stiffness of
the pars flaccida and essentially "open circuits" the acoustic shunt path provided by the
pars flaccida (see Figures 1-7 and 1-8); the remaining low-frequency input admittance
thus consists of the series combination of YCAV and YTOC. From Figure 3-6, it is
evident that such modification primarily affects the input admittance at frequencies below 700 Hz, where the low-frequency resonance seen near that frequency in the flaccida
intact ears is entirely eliminated and the acoustic compliance below the resonance frequency is decreased from a mean value of 1.13 x 10-
3
mm 3 / Pa to 0.79 x 10- 3 mm 3 /Pa,
matching the acoustic compliance of YI at frequencies above the resonance (0.80 x 10- 3
mm 3 /Pa). These results, along with the pars flaccida removed measurements, are con-
sistent with the middle ear model, with compliances of the cavity, parsflaccida, and pars
5
This method of computing model parameter directly from admittance plot works only for the simplest
case--such as YIR, which has only one parameter CCAV. Other parameters discussed in this chapter
were computed using the least-square model fitting technique discussed in Chapter 4.
89
tensa-ossicular-cochlear of 1.67 x 10- 3 mmn3 /Pa, 1.99 x 10-
3
mm 3 IPa, and 1.51 x 10- 3
mm 3 /Pa respectively.
The location of the low-frequency resonance further allows us to compute the acoustic
mass of the pars flaccida. Its role in generating such resonance is clearly demonstrated
by the disappearance of the sharp magnitude peak and angle change in the pars flaccida
stiffened ear. Assuming that this resonance is generated by the series interaction between
the flaccida's compliance and acoustic mass, the following equation governs the location
of the resulting resonance:
fresonance
=
1
27r rL pFCpF
(3.2)
With the mean measured resonance frequency of 480 Hz, the corresponding acoustic
mass, LPF, thus has a value of 0.55 g/cm4 . Assuming that the pars flaccida is circular
with a radius of 0.8 mm (in agreement with our flaccida area measurement of 1.95 mm 2 ),
the estimated mechanical mass of the parsflaccida is 0.55 x Area2 (in cm 4 ) = 2.2 x 10-4g.
Further assuming that the average density of the pars flaccida is that of water, lg/cm3,
we can compute an estimated thickness of the pars flaccida of 0.11 mm. This estimated
thickness is consistent with anatomical measurements.
3.1.5
Input admittance with and without manipulation to pars flaccida
-
bulla hole open
Measurements of the middle-ear input impedance with the bulla wall intact but with
the probe tube hole open were made in the left ear of five gerbils (Al, A2, B1, B2, B3)
and the right ear of three gerbils (B5, B8, B9). Out of these eight ears, only A2, B8,
and B9 were measured with the TM undisturbed and with the pars flaccida stiffened.
Figure 3-7 shows the input admittance measurements made in the left ears of gerbils B8
and B9. Two plots are displayed in each figure; one was measured with the tympanic
membrane intact and undisturbed, yHO and the other one was measured with the pars
flaccida stiffened, yHFSO
.
Regardless of the conditions of the pars flaccida, the input
admittances are stiffness dominated at frequencies below 300 Hz, where the admittances
increase proportionally with frequency, and the angles are near 900.
(b) Gerbil B9
(a) Gerbil B8
010
0)
CO
C.
Eo
10
E
100
q•
W M)
-0
C. -90
..- 90
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure 3-7: The middle-ear input admittance measured in the right ears of gerbils B8
and B9-with the bulla wall intact but the probe-tube hole open. Two measurements
are shown in this figure: one was obtained with a normal and undisturbed tympanic
membrane yHO, the other one was measured with the pars flaccida stiffened yHO
FS
The alphanumeric characters (which are enclosed in parentheses) following each legend
indicate the switch positions used to represent the particular experimental manipulations
(see Figure 2-18).
The changes produced by stiffening the pars flaccida in this configuration are very
91
similar to the changes produced in the intact middle ear. The low frequency compliance
is decreased and the resonance near 400 Hz disappears. With the tympanic membrane
undisturbed, the mean low-frequency compliance was found to be 3.69 x 10-
mm 3 /pa;
while the ears with the pars flaccida stiffened have a mean compliance of 1.71 x 10- 3 mm 3 /Pa.
Stiffening pars flaccida had little effect at frequencies greater than 800 Hz.
According to our model, the compliance of the open-hole-flaccida-stiffened condition should be a direct measurement of the compliance of the pars tensa, while the
open-hole-flaccida-intact condition should represent the sum of the flaccida and tensa
compliances.
CPF =
This model than suggests that CTOC = 1.71
x
10- 3 mm 3 /Pa and
1.98 x 10- 3 mm 3 /Pa, values that are nearly identical with the compliances
estimated from the middle-ear intact measurements made on these same ears (Section
3.1.4).
3.1.6
Input admittance before and after manipulation of pars flaccida
-
middle ear widely opened
In the left ears of six gerbils (B1,
B2, B3, B5, B8, B9), as much as possible of the bulla
walls were removed. The middle-ear input admittance measurements made in the left
ears of B8 and B9 are shown in Figure 3-8. Again, two measurements are displayed
in each figure, one measurement with the tympanic membrane intact and undisturbed,
yWO, and the other measurement with the pars flaccida stiffened, yWO. The input
FS
admittances in these two ears share many common features with the measurements made
in the hole-open configuration. In both ears, the differences in the magnitudes of yWO
and yWO are evident at frequencies below 600 Hz. The differences in phase can be
seenat frequencies below 2 kHz.
Changing the property of the pars flaccida did not
seen at frequencies below 2 kHz. Changing the property of the pars flaccida did not
significantly affect the admittance magnitude or phase beyond those frequencies.
(b) Gerbil B9
(a) Gerbil B8
02
10
O
(C)
4-0
E
00
"-•
<10
U)90
_0
0
CD
U)
¢0n
-90
10
2
10
3
Frequency (Hz)
10
4
10
2
3
10
Frequency (Hz)
4
10
Figure 3-8: The middle-ear input admittance measured in the left ears of gerbils B8 and
B9-bulla wall widely opened. Two different measurements are shown in this figure:
one was obtained with the tympanic membrane intact and undisturbed yWO, the other
one was measured with the pars flaccida stiffened YW 0 . The alphanumeric characters
(which are enclosed in parentheses) following each legend indicate the switch positions
used to represent the particular experimental manipulations (see Figure 2-18).
The major difference between this measurement configuration and the case of leaving the probe-tube hole open is the range of frequencies where the middle-ear cavity
admittance can be considered "shorted out." Ideally, widely opening the bulla involves
removal of all enclosing structures of the middle ear cavity, such that the effect of the cavity on the input admittance can be eliminated entirely. In practice, the presence of large
blood vessels limits the removal of the bone to only the postero-lateral and ventro-lateral
surface of the bulla wall. This limitation will be demonstrated in middle-ear pressure
measurements made in these ears (Section 3.1.8), where it is clear that the short-circuit
assumption is not valid at frequencies above 6 kHz - the frequency at which the effective
acoustic mass of the widely opened hole resonates with the middle-ear cavity compliance.
Above this resonance frequency, the widely opened hole is essentially an effective open
circuit (i.e. the cavity is acoustically closed), allowing the cavity admittance to be added
serially to the input admittance in the same manner as the intact middle ear.
For the case of undisturbed tympanic membrane, the mean compliance of the two ears
was found to be 4.26 x 10- 3 mm 3 /Pa. With the parsflaccida stiffened, the mean compliance decreased to 1.98 x 10- 3 Pa/mm3 . Again, the parsflaccida resonance observed in
the ears with normal TM disappears when the pars flaccida is stiffened, consistent with
the discussion of the previous section. The input admittances remain stiffness dominated
in the frequency range of 600 Hz to 1.5 kHz. The stiffness in this range is unaffected
by the condition of the pars flaccida, and is approximately equal to the low-frequency
stiffness of the ears with the pars flaccida stiffened, CTOC. These data and model yield
3
-3
estimates of CTOC and CPF of 1.98 x 10- 3 mm 3 /Pa and 2.28 x 10 mm /Pa
3.1.7
Effects of removing the pars flaccida "shield" on middle-ear input
admittance
To confirm that the stiffening of pars flaccida is indeed the cause of the reduction in lowfrequency admittance and the disappearance of low-frequency resonance, we measured
the middle-ear input admittance following the removal of the dental acrylic shield used
to stiffen the flaccida. Figure 3-9 shows the admittance measured in the left ear of gerbil
A2, where measurements were made with tympanic membrane undisturbed yHO, with
the pars flaccida stiffened yHO, and with the dental acrylic removed YAHRO
FS'AR
In this ear, as with most of the earlier measurements, tie effects of drying on the
middle-ear input admittance were not fully recognized. Therefore, the tympanic membrane was not regularly moistened, and the low frequency resonance measured in this ear
is of higher frequency and lower sharpness than most later measurements. Nonetheless,
the effects of stiffening pars flaccida are clearly visible in this figure, with the expected
reduction in low-frequency compliance and the elimination of low-frequency resonance
clearly demonstrated in YHSO . With the dental acrylic removed, the input-admittance
clearly reverted to the general features of the pre-stiffened condition, with a prominent
low-frequency resonance and an increase in low-frequency compliance. This result is consistent with our assumption that the addition of dental acrylic is responsible for stiffening
the pars flaccida and the removal of this acoustic shunt path.
Several differences do exist between the undisturbed ear and the ear with the dental
HOis
acrylic removed. The low-frequency admittance of YAR
greater
dB greater
is approximately
approximately 1I dB
than yHO indicating greater compliance of the pars flaccida. This phenomenon is
probably due to the moistening effect of the vaseline, which was used to hold the dental
acrylic in place but was mostly removed along with the acrylic. Another noticeable
difference is the increase in the resonance frequency in the unstiffened ear, an indication
of a decrease in the acoustic mass of pars flaccida -
maybe a result of the dehydration
process. At higher frequencies, the slight shift in the resonance near 2 kHz cannot be
explained in terms of the pars flaccida manipulations. We can only speculate about the
cause of this change; for example, this feature is consistent with a smaller probe-tube
hole, presumably covered by leftover vaseline during the measurement process.
c-
0
10
CO
0
CD
t-9
a)
CO
"EO
<
100
90
(D
co)
a)
0)
C,)
-90
102
10 3
10 4
Frequency (Hz)
Figure 3-9: Effects of removing dental acrylic on the middle-ear input admittance. These
measurements were made in the left ear of gerbil A2, with the probe-tube hole left open.
Three plots are shown in this figure, one with the tympanic membrane undisturbed,
one with the pars flaccida stiffened by dental acrylic, and a third one with the acrylic
removed.
3.1.8
Pressure measurements in the ear canal and the middle-ear cavity
Our results thus far have primarily been compared with the middle-ear model shown in
Figure 1-7 and 1-8. For such discussion to be meaningful, it is essential for the circuit
representation to accurately depict the actual middle-ear pressure transmission. A simple
but important test of the middle-ear model is to measure the sound pressures in both the
ear canal and the middle-ear cavity, and compare these measurements with the predicted
values based on the admittance measurements discussed in the previous sections.
Figure 3-10 shows the middle-ear to ear-canal pressure ratios measured in the right
ears of gerbils B8 and B9 under three conditions: 1) with the tympanic membrane
intact and undisturbed, 2) with the pars flaccida stiffened, and 3) with the parsflaccida
removed. In the preparation of these figures, the measured ear-canal pressure levels have
been corrected for the residual ear-canal volume using the two-port model described in
Section 3.1.1. In the low-frequency region, where the pressures at both ear-canal and
middle ear are in phase, the sound pressure levels are determined by a simple voltage
divider between the compliance of the middle-ear cavity CCAV and the compliance of
the tympanic membrane-ossicular-cochlear complex (CToc or CPF+CTocdepending on
the condition of the pars flaccida). The measured pressure ratios thus provide a means
of determining the relative stiffness between these compliances, specifically:
IPMECI
_
IPECI PFstiffened
CTOC
CTOC + CCAV
and
IPMEcI
IPECl
CTOC+ CPF
CPF(3.4)
IECI TMundisturbed
CTOC
CCAV
TMundisturbed
CTOG CCAV +CPF
(33)
(a) Gerbil B8
(b)Gerbil B9
1
0
O
w
0~
LJ10
ai)
O
L.
(/)
c/j)
U/)
13..
CO)
U.)
U3)
00
-90
)-180
(.C
CL--180
100
1000
Frequency (Hz)
100
1000
Frequency (Hz)
Figure 3-10: Middle-ear cavity to ear-canal pressure ratio measured in the right ears of
gerbils B8 and B9-middle ear intact. The pressure ratios were measured under three
conditions: 1) with the tympanic membrane intact and undisturbed, 2) with the pars
flaccida stiffened, and 3) with the pars flaccida removed. The alphanumeric characters
(which are enclosed in parentheses) following each legend indicate the switch positions
used to represent the particular experimental manipulations (see Figure 2-18).
For measurements made in the right ear of gerbil B8, the measured pressures are
in-phase at frequencies below 300 Hz. In this range, the pressure ratio measured with
pars flaccida removed is near unity, confirming that the hole made in the pars flaccida
was indeed acting as open circuit, and that the middle-ear and ear-canal microphones
were properly calibrated. For the case where the pars flaccida is stiffened, the measured
pressure ratio is approximately 0.46, close to the value of 0.44 calculated from Eqn. 3.3
and the data of Figure 3-6a 6 . The measured low-frequency pressure ratio when the tympanic membrane is undisturbed has a magnitude of approximately 0.73, which compares
well with the model prediction of 0.69. 7 The measurements made in gerbil B9 share most
of the general features observed in gerbil B8. At frequencies below 300 Hz, the measured
pressure ratios for cases of pars flaccida removed, stiffened, and undisturbed are 0.01,
0.50, and 0.68 respectively. These measured values are very close to the model predictions
of 0.00, 0.50, and 0.66.8 The close agreement between the predicted pressure ratios and
the measured values in both ears confirms the validity of the series configuration between
the cavity admittance and the admittance of the tympanic membrane-ossicular-cochlear
complex, at least in the low-frequency region.
The admittance and the pressure measurement results all demonstrate that the pars
flaccida, the pars tensa-ossicular-cochlear complex, and the middle-ear cavity all have
compliances of comparable magnitude, with the pars flaccida having a slightly greater
value than the other two. Consequently, in the series topology, the cavity compliance is
less than half the compliance of the overall tympanic membrane-ossicular-cochlear com6
CTOC = 1.32 x 10 - 3 mm 3 IPa and CCAV = 1.66 x 10 - 3 mm 3 /Pa.
'Prediction is based on Eqn. 3.4, with CPF = 2.45 x 10- 3 mm 3 /Pa and the same CTOC and CCAV
as above.
8
Model prediction values were obtained from Figure 3-6b, where CTOC = 1.68 x 10 - 3
- 3
mm 3 /Pa.
mm 3 /Pa and CCAV = 1.66 x 10
CPF = 1.51 x 10
3
mm 3 /Pa,
plex. Thus, the cavity compliance tends to dominate the low-frequency input admittance
of the intact middle ear, as demonstrated in Figures 3-3 and 3-4.
Figure 3-11 shows the middle-ear cavity to ear-canal pressure ratio measured in
the left ears of gerbils B8 and B9, where the middle-ear cavities were widely opened.
In the middle-ear model, widely opening the middle-ear cavity should "short" out the
admittance of the cavity, causing the middle-ear pressure to be uniformly zero. However,
the loading effect of the radiation impedance and the incomplete opening of all bulla walls
resulted in the generation of finite sound pressure in the middle ear cavity. Figure 311 shows that at frequencies above 4 kHz, the separation between the ear-canal and the
middle-ear pressures is less than 20 dB, proving that the "short circuit" assumption does
not apply in this frequency range. The frequency of the pressure maxima agrees well
with the frequency of middle-ear admittance minima measured with middle ear widely
opened (Figure 3-8).
Consistent with the admittance measurements, the pressure ratios at frequencies
above 500 Hz do not differ significantly between the case where the tympanic membrane
is undisturbed and case where the parsflaccida is stiffened. Below 500 Hz, the ears with
normal tympanic membrane show approximately 10 dB higher middle ear pressure than
the ears with pars flaccida stiffened. Such results confirm the shunt path configuration
between the pars flaccida and the pars tensa-ossicular-cochlear complex, where substantial volume velocity can be channeled through the shunt path to produce higher pressure
in the middle ear.
100
(b)Gerbil B9
(a) Gerbil B8
10
0
CL
10
O
0IJJ
10
-2
10 -3
lO1
180
90
0
-90
-180
10
10
4
Frequency (Hz)
2
10
3
10
Frequency (Hz)
Figure 3-11: Middle-ear cavity to ear-canal pressure ratio measured in the left ears
of gerbils B8 and B9-middle ear widely opened. The pressure ratios were measured
under two conditions: 1) with the tympanic membrane intact and undisturbed, and 2)
with the pars flaccida stiffened. The alphanumeric characters (which are enclosed in
parentheses) following each legend indicate the switch positions used to represent the
particular experimental manipulations (see Figure 2-18).
101
3.2
Cochlear potential measurements
One major assumption of the middle ear model of Figure 1-7 is that input to the inner ear is strictly dependent on the pressure difference across the tympanic membrane.
This premise assumes that the difference in pressure produces a proportional vibration
velocity of the ossicles, which induces an equally proportional vibration in the cochlear
fluid -
the principle stimulus that triggers the neural transduction mechanism of the
inner ear. Moller (1963; 1965) showed that over a limited frequency range, the cochlear
potential measured near the round window is approximately proportional to the velocity
of stapes vibration. Thus CP measurements provide a means of measuring the output
of the middle-ear transmission process. Two important factors must first be considered,
however, before the gerbil measurement system can be used for such a purpose: 1) The
appropriate stimulus paradigm, and 2) The presence of nonlinearity in the round-window
cochlear potential.
3.2.1
Linearity of cochlear potential measurements
As described in Section 2.4, the non-stationary behavior of round-window cochlear potential renders the chirp stimulus unsuitable for the measurement of cochlear response.
Figure 3-12 shows examples of measured cochlear potentials in response to chirp stimuli,
where the resulting nonlinearities produce sharp dips in the potential measurements,
mostly at frequencies below 1 kHz. Consequently, all other results presented in this
section were measured with tone-sweep stimuli.
The measured AC round-window cochlear potential actually consists of two components, cochlear microphonic and neural action potential (Dallos et al. , 1974). Cochlear
microphonic is derived from the ionic current flowing through the outer hair cells, and is
102
102
4.
4-'
0
a
0
Q.
101
a180
0
0
090
100
180
C/"
90
a)
(D
CD
a. -90
-180
103
102
104
Frequency (Hz)
Figure 3-12: Examples of cochlear potential responses to chirp stimuli. The nonlinearity
of the cochlear potential responses to chirp stimuli is evident in this figure. These
particular responses were obtained from the right ear of gerbil B8, with the lfs driven
by the voltage levels shown in the legend. While the applied pressure levels were evenly
spaced at 5 dB apart, the responses did not follow the same linear spacing.
103
the component of cochlear potential that actually follows the vibration of the cochlear
fluid. On the other hand, the neural action potential is due to the all-or-none firing
of the auditory nerve fibers -
a highly nonlinear process. Figures 3-13a and 3-14B
clearly illustrate this nonlinear phenomenon. In Figure 3-13a, the low intensity cochlear
potentials are dominated by neuronal firings, resulting in the observed nonlinear relationship between cochlear potentials and sound pressure levels. In 3-14B, the neural
firings produced a regular distortion in the cochlear potential.
TTX (Tetrodotoxin, from Sigma Chemical Co.), a chemical that blocks neural action
potentials but has no effect on the outer hair cells, was used to eliminate the neuronal
component from the cochlear potential in two ears, the left ears of gerbil B10 and B11.
1 mg of TTX was mixed with 1 ml of artificial perilymph to obtain a 3.13 mM solution. 1 /tl of this solution was added to the round window niche, where it diffused
through the round-window membrane into the inner ear. The effects of TTX on cochlear
potential are demonstrated in Figures 3-13 and 3-14. Figure 3-14A shows the sound
pressure level measured in the external ear canal. Figure 3-14B shows the corresponding
pre-TTX cochlear potential response, where the phase-locked neural action potential is
clearly visible. The neural component was eliminated in the post-TTX measurements,
as displayed in 3-14C.
Figure 3-13b shows the level functions of the growth of post-TTX cochlear potentials
with increasing stimulus pressure levels. The results show great improvement in the
linearity of the cochlear responses, where the neural components no longer dominate
the low-stimulus cochlear potentials. Some lesser nonlinearities, however, are still visible
in the measured responses. The cochlear potential level functions at 220 Hz, 244 Hz,
330 Hz, and 488 Hz all have slopes of greater than 1. Such nonlinearity is mainly limited
104
(b)Post-TTX
(a) Pre-TTX
II
I
I
I
I
I
.
I
.
. . . . . . . . . . .........
II
I
Slope
................... ......... i......... i... . .. ......... .... . ..i . . . .
0.
I
1....
.....
.......... .....
........i......i.. . . . i. . . . . V.....
..!..
/
--.........
i .........
i...........
...
4 i ..........
i.. . . ...........
o10
..
...
..
..
..
/....
....... .....
. - - 2 4 H
./i.......
----- -------. . . ..........( ......... ....... ....
Hz
220 Hz
-A - 122
......... .................. -+--B- 244 Hz
-.- 330 Hz
-0- 488 Hz
-*- 977 Hz
-----Hz .....
..........
........ :.......... i........
292 Hz
--
-e- 1000 Hz
180
.. ............
U)-90
p
0)
i.........
. .........
•......... •....................
. .........
... .. .......
i., i .
!.
i
I.
i
. ...
I
......... .......... ........................ .....................................
.....
....
...... i..........;.............
.....•
.
'....
....
•-! .~........
i.........
i.........
i.........
I
-90
..... .I. =.... . Ii
i
,
*'
........ ....................
". . . ... .. ...*..........
......:.........
........ i..........
.'.........
.......
..-.
.............
......
.....
.......
i..........
..
...
i.........
..
i........
......
.
.....
. . . ...... ....... .:. . . .. . . . ..i.. .. .. •. .. . . . . . . .
-180
40
50
60
50
70
Sound pressure (dB SPL)
60
70
80
Sound pressure (dB SPL)
Figure 3-13: Plots of cochlear potentials versus sound pressure levels before and after
the application of TTX. The measurements were made with tonal stimuli in the left ear
of gerbil B11. (a) The nonlinearity, especially at low sound levels, are evident at the
two measured frequencies. (b) The linearity of the cochlear potentials has been greatly
improved in comparison with the pre-TTX measurements. The cochlear potentials at
220 Hz, 244 Hz, 330 Hz, and 488 Hz still exhibit some nonlinearities, where the slopes
are all slightly greater than one. Figure 3-15 and 3-16 show that this type of nonlinearity
is limited to frequency between 200 and 600 Hz.
105
-2.0
0.
E
-1.0
a!)
W/
0.0
1 .0
Cn
• 1.0
-0
(D
O
CO)
2.0
20
10
"-
0
I01
0
-10
-20
10
10
0
-10
0
10
20
30
40
Time (msec)
Figure 3-14: Effects of TTX on the cochlear potential recording. These measurements
were obtained from the left ear of gerbil B10, where most of the bulla wall has been
removed. Top (A): The tone burst stimulus applied at the gerbil ear canal. Middle (B):
Cochlear potential response to the tone burst stimulus before the application of TTX.
Bottom (C): Cochlear potential response after the application of TTX.
106
(a) Sound Pressure Levels
(b) Cochlear Potential
10
2
-10
0
10
40
180
180
90
rn
0
0
W
-90
Ca-90
-180
0_
-180
I
M
70
a)
-"
'0
0)
N
S -10 - - - - - -
-
-- -
-
E
0)
2
10
-
-5 ,
.
010
-Z
-15
S
I "
'
I
....
1000
I
.
.
.
" 1I
.'
1000
Frequency (Hz)
Frequency (Hz)
Figure 3-15: Stimulus pressure levels and post-TTX cochlear potential responses measured in the left ear of gerbil B11 (middle ear widely opened). (a) The first two plots
display the sound pressure levels at the gerbil ear canal when different amplitudes of
tone-sweep voltages were applied to the lfs. All measurements were made in ear with
normal tympanic membrane. The bottom plot represents the pressure levels normalized
by the pressure measurements made with 10 mV driver voltage. (b) The cochlear potential measurements correspond to the pressure stimuli shown in panel (a). The bottom
plot represents the measured cochlear potentials normalized by the cochlear response
made with 10 mV driver voltage.
107
Middle Ear Widely Opened
II
I
I
I
0.0t
"10
0
%_
.1-0
Ca)
CU
10
S1.0ImV
Q.
O
180
Co
V)
.....
5.
.
..
.
-
ti)
L_c
-
0o
-
C)
-90
C,
8
O.. -180
. 100
.o
10
1000
Frequency (Hz)
Figure 3-16: Middle-ear transfer function at various stimulus levels (gerbil Bl1). The
transfer function is defined with the ear-canal sound pressure level as input and the
round-window cochlear potential as output. They are computed by dividing the cochlear
potential spectra of Figure 3-15b with the pressure spectra of Figure 3-15a.
108
to frequencies between 200 and 600 Hz, as illustrated in the tone-sweep measurements
of Figures 3-15 and 3-16. Figure 3-15b shows the cochlear potential spectra measured
with four different stimulus settings, with the corresponding ear-canal sound pressure
levels shown in Figure 3-15a. In both figures, the bottom plots show the respective
normalized spectra magnitudes, which allow easy identification of any nonlinearity across
the whole frequency spectrum. The normalized cochlear potential spectra demonstrate
the above mentioned nonlinearity between 200 and 600 Hz, with the cochlear potential
apparently suppressed at low sound intensity. The stimulus pressure also shows signs
of some slightly nonlinear behavior; however, this nonlinearity is most apparent in the
mid to high frequencies. The origin of this nonlinearity is unknown but may be in the
instrumentation.
A better way of determining the linearity of a system is to plot the system transfer
function at various stimulus levels. Figure 3-16 displays such a plot for the middleear transfer function, defined with the ear-canal sound pressure level as input and the
round-window cochlear potential as output. The transfer functions show good consistency (which is an indication of linearity) for most of the frequency range, with the
exception of the frequency range from 200 to 600 Hz, where the suppressed cochlear
potential phenomena at low sound intensity is manifested as deeper and deeper dips in
the transfer function. The magnitude of this nonlinearity is significant. The transferfunction magnitude at 300 Hz varies by a factor of 3, while the stimulus voltage varies
by a factor of 5.
109
3.2.2
Effects of pars flaccida manipulation on round-window cochlear
potential
In the left ears of gerbil B10 and Bl1, where the middle-ear cavities were widely opened,
the post-TTX cochlear potential before and after the stiffening of pars flaccida were
measured. Figures 3-17 and 3-18 show the ear-canal sound pressure levels measured in
these two ears, where the earphone driver voltage was kept constant at 10 mV during
the measurement process. As expected from the admittance results of Section 3.1, at
frequencies below the pars flaccida resonance, the measured ear-canal sound pressure
levels in the stiffened ears have larger magnitude than the undisturbed ears -
a direct
result of the increased stiffness following the removal of the pars flaccida compliance. At
frequencies above the resonance, the sound pressure levels are approximately equal for
both measurement configurations.
Using the acoustic calibration methods described in Chapter 2, these pressure spectra
can be used to compute the middle-ear input admittance of the two measured ears
(Figure 3-19). Since the tone-sweep paradigm consists of only five tonal stimuli per
octave, the frequency resolution of these input admittance plots is substantially lower
than the admittance measured with the chirp paradigm. Nonetheless, the results do
capture several important features of the effects of pars flaccida in the functioning of
the middle ear. Figure 3-19 shares many similar features with the other admittances
measured with the middle ear widely opened (Section 3.1.6), where the stiffening of
pars flaccida suppresses the overall low frequency compliance and eliminates the lowfrequency resonance. Note however that the frequency of the pars flaccida resonance
of Bl1 is slightly higher than that observed in either B8, B9, or B10 (Figures 3-8 and
3-19a), and the difference in low-frequency admittance between the stiffened and the
110
(b)Cochlear Potential
(a) Sound Pressure Levels
90
_J
C. 80
10
70
U)
(n
a)
L_
0
-0 60
0
10
0
CO
50
180
180
a,)
a,
(D
(,
(D
L,
(-.3
CD
(D
(D
(n
-90
0-.
-c
0)
S-90
-8
-180
-180
100
100
1000
1000
Frequency (Hz)
Frequency (Hz)
Figure 3-17: The tone-sweep stimulus spectra and cochlear potential responses measured
in the left ear of gerbil B10 (middle ear widely opened). (a) This plot shows the sound
pressure levels at the gerbil ear canal when voltages of constant amplitude (10 mV) were
applied to the lfs. At frequencies below 600 Hz, the generated sound pressure in the pars
flaccida stiffened ear is approximately 4 dB higher than the sound pressure generated in
the normal ear - a result of the increased stiffness at that frequency region. (b) The
general features of the cochlear responses are similar to that of the stimulus, where the
difference in pressure levels at low frequency directly translated to a similar separation
in measured cochlear response. No obvious nonlinearity is evident. The markers along
the plots indicate the frequencies of the stimuli.
111
(a) Sound Pressure Levels
(b)Cochlear Potential
0~
CD.
0
m
13...
CM
CD)
C"
0)
180
180
0)
0)
180
0)
U)
90
90
0
0
-90
-90
a-..
180
-180
1000
1000
Frequency (Hz)
Frequency (Hz)
Figure 3-18: The tone-sweep stimulus spectra and cochlear potential responses measured
in the left ear of gerbil B11 (middle ear widely opened). (a) This plot shows the sound
pressure levels at the gerbil ear canal when voltages of constant amplitude (10 mV) were
applied to the lfs. At frequencies below 600 Hz, the generated sound pressure in the pars
flaccida stiffened ear is approximately 4 dB higher than the sound pressure generated in
the normal ear - a result of the increased stiffness at that frequency region. (b) The
general features of the cochlear responses are similar to that of the stimulus, where the
difference in pressure levels at low frequency directly translated to a similar separation
in measured cochlear response. No obvious nonlinearity is evident. The markers along
the plots indicate the frequencies of the stimuli.
112
normal conditions is also smaller in this ear than the other three. Such phenomena
indicate that the pars flaccida of Bl1 may have been slightly dehydrated during the
measurement process.
Figures 3-17b and 3-18b show the cochlear potentials measured in gerbils B10 and
B11 in response to the pressure stimuli of Figures 3-17a and 3-18a.
At frequencies
below the pars flaccida resonance, the difference in ear-canal pressure levels translated
to a similar separation in the measured cochlear responses; at higher frequencies, where
the sound pressure levels are approximately equal, the resulting cochlear potentials are
also equal under the two measurement conditions. This finding is consistent with the
middle ear model: when the middle ear is widely opened, the pressure difference across
the tympanic membrane is approximated by PEC, which we assume to be the effective
input to the inner ear. Therefore, the model predicts a proportionality between PEC
and CP. One region where CP and PEC are not proportional is near the 400 Hz dip in
CP in ear B10. This dip is much deeper that that observed in PEC in this ear. This dip
may be the result of a continuing nonlinearity in cochlear potential measurements, or
it may indicate that the model separation of pars flaccida and pars tensa into separate
blocks is not accurate near resonance.
A better quantitative understanding of middle-ear transmission properties can be
gained from the transfer function of ear-canal pressure to cochlear potential response.
Figure 3-20 shows the left ears transfer functions of gerbils B10 and Bl1, both before and
after the stiffening of parsflaccida. The transfer functions were calculated from measurements made with the earphone driver voltage set at constant amplitude of 10 mV (this
is the only stimulus level where the pars flaccida stiffened measurements were made).
For frequencies below 1 kHz, the middle-ear transfer functions (with the exception of
113
(a) Gerbil B10
(b) Gerbil B11
O
0
(I)
0
0
C
CZ)10
E
0
C
010
VJV
&
0)
a)
V0
0
•I)
C,)
-C -90
CL
100
1000
100
Frequency (Hz)
1000
Frequency (Hz)
Figure 3-19: Middle-ear input admittance measured in the left ears of gerbils B10 and
B11-middle ear widely opened. (a) The admittance plots of gerbil B10 were calculated
from the ear-canal pressure measurement of Figure 3-17a. The effects of the stiffened
parsflaccida on the low-frequency admittance is apparent in this figure, with the familiar
parsflaccida resonance and compliance entirely suppressed. The markers along the plots
indicate the frequencies of the stimuli. (b) The admittance plots of gerbil B11 were
calculated from the ear-canal pressure measurement of Figure 3-18a. The effects of pars
flaccida on the low-frequency admittance is again apparent in this figure. Note that
the low-frequency resonance in this ear is higher than the measurements of B8, B9, and
BO10 (Figures 3-8 and 3-19a). The difference in low-frequency admittance between the
stiffened and the normal configuration is also lower than the other three ears. All these
phenomena show that the tympanic membrane may have been slightly dehydrated when
the measurements were made. The markers along the plots indicate the frequencies of
the stimuli.
114
the undisturbed ear of gerbil B10) are all stiffness dominated, where the magnitudes are
generally proportional with frequency, and the angles are between 450 to 90'. For gerbil
110, the transfer function of the undisturbed ear shows a dip between 200 and 600 Hz,
a result of the unexpected decrease in cochlear potential in this frequency range (see
Figure 3-17b). This feature shares some similarities but also some differences with the
nonlinear cochlear potential observed in gerbil Bl1.
While all these features occur at
the same frequency range, the sharp dip in cochlear response at approximately 400 Hz
is noticeably absent in the B11 measurements. Also, the amount of cochlear potential
decrease, after correction for the difference in ear-canal pressure levels, is substantially
larger in BO10 than the reduction shown in B11. Besides this peculiarity, the two transfer
functions exhibit most of the characteristics predicted by the middle ear model. Recall
from the pressure ratio measurements of Figure 3-11 that with the middle ear cavity
widely opened, PEC > PMEC at frequencies below 5 kHz; thus, the bulla cavity is
essentially shorted out in this frequency range. As a result, the middle-ear model consists of only pars flaccida in parallel with the pars tensa-ossicular-cochlear complex. In
this configuration, the volume velocity entering the inner ear is only dependent on the
pressure of the ear canal, and independent of the pars flaccida. Such characteristics
are clearly demonstrated by the measured middle-ear transfer ratio, where the pre- and
post-stiffened ears show great similarity in both magnitudes and angles. This similarity
suggests that any modulation of ear-canal pressure by the acoustic properties of pars
flaccida (i.e. increasing the low-frequency input admittance and decreasing the sound
pressure) produces a similar modulation of the input to the cochlea.
To compare the relative effects of pars flaccida stiffening on the middle-ear input
admittance, ear-canal pressure level, and cochlear potential generation, we computed the
115
(a) Gerbil B10
(b) Gerbil B11
N a tol,|
I
.
f
i
a s@.l
3
>10
ulo
S-0
Pars flaccida
stiffened
CW 0 2
L.-
F-
* I II
10
A I I I I aa"
IlhIhlEul
I
I
I
|11
1
90
0
-90
-180
..........
100
100
1000
Frequency (Hz)
-
..........
1000
Frequency (Hz)
Figure 3-20: Middle-ear transfer functions of gerbils B10 and B11 (middle-ear cavity
widely open). The transfer functions before and after the stiffening of pars flaccida are
shown in this figure. The measurements were made with the earphone driver voltage set
at constant amplitude of 10 mV. The markers along the plots indicate the frequencies
of the tonal stimuli.
116
ratio between the pre- and post-stiffening results of each of these measurements. The
changes in the cochlear potentials and sound pressure levels were obtained by taking the
ratios (in (dB) between the measurements made in the normal ear and the measurements
made in the stiffened ear. It is important to realize that the measurements used for
these computations were produced by applying a constant voltage to the earphone, which
essentially acted as a constant volume velocity source in parallel with an internal source
admittance. The results of these computation would have been different if a constant
pressure source was used instead (see Section 4.5 for a more complete discussion on this
topic).
ACP = 20log CPIFS,constant V
ACP
APEC V
2log
(3.5)
CPlconstant V
SI
FS,coristant V
2010g l Pf SconstantV
(3.6)
IY!
PIconstantV
AY = 20 log
(3.7)
YIFS
The subscript V is used to indicate that constant voltage was applied to the earphone
in the measurement process. Since AY is not sensitive to the source type, no subscript
is needed. Also note that for AY, the order of division was reversed. This is due to
the fact that increasing admittance actually decreases sound pressure level as well as
cochlear potential response. Analysis based on Equations 3.5-3.7 allows us to quantitatively characterize the pars flaccida contributions to each of the three quantities, and to
compare the relative variation among these contributions. Figure 3-21 shows the results
from measurements made in gerbil B10 and Bl1, plotted in dBs of magnitude. Except
for the noted anomaly of the cochlear potential measurement at frequencies between 200
and 600 Hz in gerbil B10, all three computed quantities are equal to within
117
+
2 dB. Such
results agree with the traditional view of the middle ear as a linear system (Guinan and
Peake, 1967; Pickles, 1988), where a linear proportionality relationship exists between
stimulus and response, and demonstrate that any of these quantities can be used as indicators of the effects of pars flaccida in the middle-ear mechanics when the middle ear is
open. At frequencies above the pars flaccida resonance (, 800 Hz), the three quantities
are all uniformly close to 0, indicating that the acoustic properties of pars flaccida do not
affect the middle ear signal transmission in this frequency range. At lower frequencies,
the presence of pars flaccida apparently causes a uniform decrease in cochlear potential
and sound pressure level, except at the resonance frequency where the amount of decrease
is sharply higher. The actual amount of low-frequency change in these two ears is fairly
different, with gerbil Bl1 showing changes of approximately 2-3 dB, while gerbil BO10
shows a far greater 10 dB difference. The small differences between AY and APEC Iv
can be explained in terms of the circuit models of the middle-ear and the sound source.
Recall from Section 2.2 that the sound source can be represented by a Norton equivalent
circuit. The pressure generated in the ear canal by the equivalent volume-velocity source
is directly proportional to the impedance (inverse of admittance) of the internal and the
measured loads, PEC = 1/(YS + YME). Therefore the change in PEC produced by a
change in middle-ear input impedance is, PEC + APEC = 1/(YS + YME + AYME).
Note that APEcIv is not proportional to 11/(AYME)I unless
lYsi
<< IYMEI.
This
condition is generally true for measurements made at low frequencies using the ifs (see
Figures 2-11 and 3-19), therefore the differences between AY and APECIV are expected
to be small.
118
(a) Gerbil BO10
(b) Gerbil B11
10
2
10
3
Frequency (Hz)
Figure 3-21: Changes in middle-ear input admittance, ear-canal sound pressure, and
cochlear potential between pre- and post-stiffened measurements in gerbils BO10 and B11.
The plots in these figures were obtained by subtracting the measurements of cochlear
potential and sound pressure level made in the normal ear from the measurements made
yWO
in the stiffened ear (all in dB). The change in admittance was calculated as 20 log
FS
This is due to the fact that increasing admittance actually decreases sound pressure level
as well as cochlear potential response.
119
120
Chapter 4
Discussion
4.1
Comparison with previously reported measurements
Middle-ear input admittance of gerbils was measured by Ravicz et al. (1992) using
methodology similar to this study. The average YI reported by Ravicz et al. is shown
in Figure 4-la along with the mean of our measurements. Both admittance means are
accompanied by their statistical 95% confidence intervals (i.e.
+
2 standard errors, with
n = 5 for Ravicz et al.'s data and n = 8 for our measurements). Good agreement exists
at frequencies below 2 kHz, where the admittance is clearly compliance dominated. The
maximum variation between the two mean measurements is on the order of 5 dB in
magnitude. This result, along with the small error bounds, indicates good consistency
in low-frequency compliance across all measured gerbil ears. The error bounds of our
measurements increase substantially in the frequency range between 3-5 kHz.
This
significant increase is mainly the result of measurements made in three ears -
Al,
Bl, and B9 -
which feature several peaks and reversals in slope along with significant
negative phase angles. These mass-like behaviors are not evident in measurements of
121
other ears, which are mainly resistance dominated -
similar to the data of Ravicz et
al. At even higher frequencies, both average measurements are resistance dominated,
with magnitudes of approximately 10 nS and phase angles near 00. Figure 4-2 shows
the t-test result that compares the similarity of these two means. For the middle ear
intact measurements, the two means are equal at 5% significant level over most of the
frequency range. Only at frequencies between 1 to 2 kHz are the two means statistically
different. From Figure 4-la, however, we see that the means are less than 2 dB apart in
this frequency range. The statistical result is mainly due to the small sample size and
the small standard errors of the two measurement sets.
Also shown in the amplitude plot of Figure 4-la is an estimate of the middle-ear input
admittance computed from the umbo velocity measurements of Cohen et al. (1993) and
the pars tensa area measurements of Rosowski et al. (1995, unpublished)[areae 8.3mm 2 ].
The Cohen data clearly do not match the others. A possible reason for this discrepancy
arises from the experimental method used by Cohen et al., where a hole was drilled into
the dorsomedial extent of the skull to reveal the umbo tip, thereby exposing the middleear cavity to the ear canal and the sound stimulus. At low frequencies, the hole would
act to reduce the pressure difference across the tympanic membrane, limit the vibration
velocity of the umbo, and reduce the middle-ear input admittance. Consequently, the
slope of this admittance estimate at low frequencies is substantially steeper than the
other measured admittances.
Ravicz et al. (1992) also reported the gerbil middle-ear input admittance measured
with the vent tube removed and the hole in the bulla left open. Their average admittance
is shown in Figure 4-1b along with our yHO measurements. One obvious difference
between the two sets of measurements is the frequency of the minimum in admittance
122
(a) Middle ear intact
(b) Bulla hole left open
.- I
O
Uo
010
0
0
U)
E
o
o
) 90
C10
CL
a) 9
-a
0
ai)
CD
_- -90
I-
10
2
10
3
10
Frequency (Hz)
Frequency (Hz)
Figure 4-1: A comparison of the measured YI and yHO with other available admittance
data. (a) The mean of all YI measurements (shown in Figure 3-3) is plotted along with
the 95% confidence interval (indicated by the fine solid lines). The admittance data from
Ravicz et al. (1992) were calculated from the measurements made in five ears, where the
middle ear cavity was vented by a long thin tube (shown in Figure 9a of that paper).
The fine dashed lines delineate the corresponding 95% confidence interval. The third
plot shows the admittance estimate calculated from the umbo velocity measurements
made by Cohen et al. (1993), assuming the area of the pars tensa is 8.3mm 2 . (b) The
mean of all yHO measurements (shown in Figure 3-4) is plotted along with the 95%
confidence interval (indicated by the fine solid lines). The admittance data from Ravicz
et al. were calculated from the measurements made in six ears, with the middle-ear vent
tube hole left open (shown in Figure 9b of that paper).
123
(a) Middle ear intact
(b) Bulla hole left open
1.2
0.9
a)
C,
0.6
CZ
to
C.
.- ' 0.3
0.0)
0.0
1000
1000
Frequency (Hz)
Frequency (Hz)
Figure 4-2: T-test comparison of the similarity between the our measured YI and yHO
with the measurements of Ravicz et al. (1992). The significance curves indicate the
probability of observing the given results by chance given that the measurement means
are equal. The "H" curves show the acceptability of the null hypothesis that the two
means are equal. "H= 1" means that we can reject the null hypothesis at 0.05 significance
level, whereas "H=0" means do not reject the null hypothesis at 0.05 significance level.
magnitude that occurs near 3 kHz. The Ravicz data show a minimum that occurs at
lower frequencies. According to Ravicz et al. (1992), this minimum results from the
anti-resonance produced by the parallel combination of the compliance of the air within
the middle-ear cavity and the acoustic inertance of the bulla hole. The magnitude of this
inertance is inversely proportional to the diameter of the bulla hole, such that a smaller
hole produces larger inertance. A larger inertance should result in a larger susceptance
magnitude, a lower resonance frequency, and a lower frequency for the minimum in
admittance magnitude. We can thereby explain the difference between the two sets of
measurements based on the size of the bulla hole. Ravicz et al. suggested that the holes
they made were approximately 1 mm in diameter, and we estimate our holes to be 1.2 mm
in diameter. Therefore, the difference in the hole size is consistent with the parallel
resonance theory. One similarity observed in both sets of measurements is the increase in
124
the size of the error bounds, especially in the low-frequency compliance-dominated region.
Consistent with the discussion in Chapter 3, such a feature is the direct result of removing
the stiffer cavity admittance, thus revealing the greater variation among the compliances
of the tympanic membrane-ossicular-cochlear complex. Except for the aforementioned
resonance frequency, both sets of measurements have overlapping confidence intervals,
and they all exhibit the general features of yHO described in Section 3.1.2.
The t-
test result shown in panel B of Figure 4-2 shows the expected rejections of the "equal
hypothesis" at the two anti-resonance frequencies of 2-3 kHz. The two means also differ
statistically at frequencies between 600 Hz and 1 kHz (the actual difference is less than
5 dB in magnitude). At other frequencies, the two sets of measurements are equal at
5% statistical significance level. One noteworthy point in the results of Ravicz et al. is
the absence of pars flaccida resonance in all but one measurement. Since the tympanic
membranes in that study were not moistened periodically, such a finding is not surprising
given the rapidly decaying resonance under conditions of dehydration.
4.2
Correlation of input admittance measurements with
middle ear models
4.2.1
General considerations
To quantify the contributions of the middle-ear anatomical structures to the measured
input admittance requires the use of a middle ear model. In chapter 3, we presented the
measured admittance data along with the discussions of some simple model parameters
that can be estimated directly from the admittance plots, such as the flaccida and the
cavity compliances. In this section, a systematic approach will be employed to estimate
125
all middle-ear parameters deemed important to the understanding of the roles of pars
flaccida in middle-ear acoustic transmission. Figure 4-3 shows the circuit model that
was used for this purpose, which includes the modeling of the pars flaccida, pars tensa,
middle-ear cavity, ossicles, and the cochlea. Variations of this model have previously been
used to explain the functioning of the middle and inner ear (Zwislocki, 1962; Zwislocki,
1963; Moller, 1961; Moller, 1965; Schmiedt and Zwislocki, 1977; Lynch et al. , 1982;
Kohll6ffel, 1984; Rosowski et al. , 1986; Rosowski et al., 1990; Rosowski, 1991; Rosowski
and Merchant, 1995). The model appears to provide adequate approximations to most
experimentally measured data.
The basic premise of this simplified series circuit model has been described in Chapter 1. Note, however, that some modifications have been made to facilitate the modeling
discussion in this chapter. The circuit elements that represent the pars tensa, the ossicles, and the cochlea have been replaced by a simplified circuit -
a series RLC network
LTOC, RTOC, and CTOC. This simplified representation of the pars tensa, ossicular and
cochlear complex (1) requires a smaller number of model parameters, and (2) adequately
represents important acoustical and mechanical features at low frequencies, such as the
stiffness of the tensa and ossicles and the damping of the cochlea (Zwislocki, 1962). The
use of the simplified representation forfeits our ability to represent more detailed acoustic variables. For example, the volume velocity entering the stapes footplate Us (which
is commonly accepted as the stimulus that directly triggers the cochlear response) can
no longer be represented by any circuit variable. Consequently, the model cochlear potential is assumed to be directly proportional to the volume velocity entering the pars
tensa-ossicular-cochlear complex, UpT. Such an assumption is justified, at least as a
first order approximation: Moller (1965) [Figure 2-17] demonstrated a proportionality
126
Pars Tensa,
Malleus,& Incus
I
I
17
Us
1
Ii
Ii
Ii
Stapes &
Cochlea
! I Ysc
_______
------------------------------- )
UT
|
UPT
|
|
-
PEI
//
/
h
/
/
LHOLE
RHOLE
Figure 4-3: Circuit representation of the series model of the middle ear. This circuit
model is a modified version of that shown in Figure 1-8. The modification is done to
facilitate the modeling discussion that will be presented in this chapter. In particular,
the circuit elements that represent the pars tensa, the ossicles, and the cochlea have been
replaced by a simplified circuit (in the form of a series RLC network). The manipulations
of the bulla wall are represented as switches in parallel with the cavity admittance:
Position "3" represents the bulla hole open configuration; Position "2" models the widely
opened cavity wall, where YCAV is assumed to be short circuited; and the intact middle
ear is represented by switch position "1". Similarly, the manipulations of the parsflaccida
is represented as a switchable admittance with three possible settings. When the pars
flaccida is intact, the switch is in position "A", where YPF acts as a shunt path across
the pars tensa-ossicular complex. Switch position "B" models the immobilized pars
flaccida, which causes all the tympanic-membrane volume velocity UT to pass through
pars tensa. Switch position "C" represents a removed pars flaccida, where it effectively
shorts out the rest of the YTOC-
127
relationship between the middle-ear input admittance and the cochlear potential over a
frequency range from 400 Hz to 2 kHz.
Another important assumption of the model is that pars flaccida and tensa are independent sound paths, in that the volume velocity through either path is completely
determined by the pressure difference across the TM and the impedance of the path.
In other words, changes in pars tensa which do not affect the pressure difference across
TM are expected to have no effect on pars flaccida and vice versa. This assumption of
independence underlies the traditional thinking that parsflaccida forms a passive shunt
path around the main ossicular transmission path of the hearing process. Tests of the
validity of this assumption are thus essential to our understanding of the roles of pars
flaccida in hearing. In this chapter, specifically in Section 4.4, we will discuss tests of
this assumption using the cochlear potential measurements in ears with widely opened
middle-ear cavities.
By using our simple scheme to represent the complex middle-ear transmission, it is
imperative to realize the possible inaccuracies and limitations in our predicted values.
First, our model does not take into account any possible relative motions between the
ossicular bones. Guinan and Peake (1967) reported that in cats, relative motions do
occur between the malleus and incus at frequencies above 5 kHz. These motions shunt
some portion of the volume velocity entering the middle ear away from the cochlea. A
second possible source of error has its origin in the mechanics of the tympanic membrane
vibrations. Khanna and Tonndorf (1970,1972) reported that at high frequencies (f >
3 kHz), eardrum vibrations tend to break up into sectional patterns, where the higher
harmonic modes of vibration reduce the transmission of high frequency power to the
middle ear. Since the tympanic membrane of gerbil is smaller than cat, we might expect
128
these deviations to occur at higher frequencies. These possible deviations from the ideal
simple model must therefore be considered when comparing the model predictions with
the measured data.
4.2.2
Estimation of model parameters
In Chapter 3, we were able to calculate the compliances of the middle-ear cavity (CCAV)
directly from the low frequency admittance data using Equation 3.1. Such an intuitive
approach cannot be directly extended to the estimations of other middle-ear model parameters, especially when the middle-ear input admittance results from the interactions
of multiple acoustic components. In this section, a more systematic optimization process is used to estimate these parameters. With the computed model parameters, we
will further demonstrate that only certain subsets of these model elements are necessary
to accurately describe the overall input admittance results.
The admittance data presented in Section 3.1 were used to estimate the seven parameters modeled in Figure 4-3 (CToc, RTOC, LTOC, CPF, RPF, LPF, CCAV). For
measurements made with the bulla hole left open, two additional parameters, RHOLE
and LHOLE, were needed to describe the resonance behavior between the middle-ear
cavity and the bulla hole.
The estimation procedure consists of three separate optimization processes, whereby
the parameter values of each admittance block are defined separately. For measurements
made with the intact middle-ear cavity, the cavity compliance (CCAv) was first determined by fitting the circuit model with the two switches at positions C and 3 (which in
effect eliminates YPF and YTOC, leaving a single capacitor CCAV in the model) to the
admittance measurement made with parsflaccida removed and middle-ear cavity intact.
129
The value of CCAV was varied to minimize the mean-square-errors between the measured
and the model admittances. This optimization procedure was implemented in Matlab
using the fmins function 1 . Since the circuit model can only accurately represent the
input admittances at low frequencies, all of the optimization computations utilize only
measurements made at frequencies below 4 kHz. The next step involved the estimation
of the pars tensa-ossicular-cochlear complex parameters -
CTOC, RTOC, LTOC. With
the first switch of the model at position B, these three parameters were optimized simultaneously by finding the best model fit to the measured admittance data obtained with
pars flaccida stiffened. Once the four parameters above were known, the compliance,
mass, and damping of the pars flaccida (CPF,LPF, RPF) can be obtained by matching
the complete model (with the first switch at position A) to the admittance measurements
made in ears with normal tympanic membranes. In all cases, the second model switch
was set at position "1" if the measurements were made in ears with middle ears intact,
or at position "2" if the measurements were made in ears with either bulla hole open or
with bulla wall removed.
Figure 4-4 compares the middle ear intact measurements made in the right ears of
gerbil B8 and B9 with the best model fits. The model parameter values are tabulated in
Table 4.1. At frequencies below 2 kHz, both the magnitude and phase of the model predictions closely resemble the shapes and numerical values of the measured admittances.
In particular, the low-frequency resonances at approximately 400 Hz are adequately
described by the simple RLC representation of the pars flaccida. However, several differences between the measurements and the model predictions can be observed.
1
At
The fmins function uses the Nelder-Meade simplex search algorithm (Nelder and Mead, 1964; Dennis
and Woods, 1987). It is a direct search method that does not require gradients or other derivative
information. See the Matlab manual or the two references for more details.
130
(a) Gerbil B8
(b) Gerbil B9
0l
U)
10
C
.)
0
0
010
E
co1
3
2
10
10
Frequency (Hz)
10
4
2
10
3
Frequency (Hz)
10
4
Figure 4-4: Comparison of the input admittances YI, YFS, and Y R measured in gerbils
B8 and B9 with the input admittances of the middle-ear circuit model. Of the six curves
presented in this figure, the three model prediction curves are labeled in the left panel,
while the right panel shows the line type used for the measurements. For YS, a simple
compliance is sufficient to represent the measured admittance at frequencies up to 2 kHz.
The deviation from compliance behavior at higher frequencies was a result of the acoustic mass and resistance created by the hole in the pars flaccida. For YI and YI,
FS the
model admittances match the measured data well at frequencies below 2 kHz. At higher
frequencies, the simple RLC circuit that represent the pars tensa-ossicular-cochlear complex is not capable of representing the fine structures observed in the actual measured
admittances.
131
frequencies above 3 kHz, clear discrepancies between the circuit model and the measurements exist for all three admittance curves in Figure 4-4. For the admittance measured
with pars flaccida removed, the masslike property of the flaccida hole is significant at
high frequencies; therefore, the short circuit assumption between the ear canal and the
middle ear cavity is not valid in this range. Assuming the admittance of the parsflaccida
hole is Y = 1/jwL, where L = po(l + 0.6r)/rr2 is the acoustic mass of the hole, the
predicted frequency where the admittance changes from compliance to mass-like is:
fr
2/7rCCAVpo(l + 0.6r)
(4.1)
Assuming that the pars flaccida is circular with radius r = 0.1 cm, and with a thickness
of I = 0.15mm, this equation predicts a resonance frequency of approximately 7 kHz.
The measurements in Figure 4-4 show that it is indeed in this frequency range that
the cavity admittance stops behaving as a compliance structure; however, there is no
observable resonance is this frequency range. Instead, the measured admittance magnitudes show a gradual plateau with several minor peaks and valleys. Such behavior
indicates that under this configuration, some resistive components may also be present
in the middle-ear system, as indicated by angle measurements that are close to 00. For
the tympanic membrane intact measurements (i.e. pars flaccida is either undisturbed or
stiffened), the simple circuit model is unable to follow the fine structures observed in the
admittance measurements at frequencies above 3 kHz. This is not surprising considering
the simplistic representation of the pars tensa-ossicular-cochlear complex.
A more accurate "broad-band" representation of YTOC can be obtained from the
admittance measurements made with the middle ear intact and pars flaccida stiffened,
132
B8
B9
B8
B9
(Right Ear)
(Right Ear)
(Right Ear)
(Right Ear)
Measurement
configuration
CTOC (10-12 m 3 /Pa)
Bulla wall
intact
1.3
Bulla hole
open
1.5
Bulla hole
open
1.9
CpF (10 - 12 m 3 /Pa)
2.4
2.3
1.7
RToc (10' Pa-s/m5 )
8.5
Bulla wall
intact
1.7
1.5
7.0
8.4
7.1
5
RPF (107 Pa-s/m )
10.3
6.7
3.8
10.9
4
LTOC (103 kg/rnm
)
4
LpF (104 kg/m )
CCAV (10 - 12 rn 3 /Pa)
2.2
9.4
1.7
2.0
13.0
1.7
1.8
8.7
1.5
5.4
-
Table 4.1: Middle-ear model parameters. These model parameters were calculated from
the admittance measurements made either with the middle-ear cavity intact or with the
bulla hole left opened. For the bulla hole open measurements, CCAV cannot be estimated
from the admittance data.
YIs
FS
1
IC
YTOC -
YFITs
FS
(4.2)
jWCCAV
Equation 4.2 is justified based on the assumption that the middle-ear cavity is in series
with the tympanic membrane-ossicular-cochlear complex, which has been verified by
numerous researchers [page 125], and will be further tested in Section 4.3. It is preferable
to calculate YTOC from Y
s
rather than YHO or YWO because of the presence of
high frequency resonance in the two later measurements - a result of the opening of the
bulla wall. The circuit model for this "broad-band" representation of YTOC is shown
in Figure 4-5.
Figure 4-6 shows the admittance predictions of this "broad-band" model. Also included in the figure are the various circuit blocks that make up the complete middle-ear
input admittance Y' -
YTOC, YCAV, and YPF. With the exception of YTOC, all
the circuit elements used to produce this figure are the same as that shown in Figure 4-4.
Comparing these individual acoustic admittances allows us to appreciate the quantitative
133
UT
r-E
UPT
LHOLE
RHOLE
Figure 4-5: Modified "broad-band" middle ear model that allows high frequency representation of the middle-ear input admittance. This model is essentially the same
as the model shown in Figure 4-3 - with the RLC network representing the pars
tensa-ossicular-cochlear complex replaced by a single broadband admittance YTOC that
is computed from the Y4 measurements.
contribution of each of these acoustic blocks to the overall middle-ear input admittance.
At frequencies below 300 Hz (below the resonance frequency of the pars flaccida), the
input admittances of all acoustic blocks are mostly compliance dominated. In this range,
the acoustic compliances of the middle-ear cavity, the pars flaccida, and the pars tensaossicular-cochlear complex are all comparable in magnitude (= 1 - 2 x 10-12m 3 /pa),
and they combine in the parallel-series configuration of the middle-ear model to produce
the overall compliance.
(4.3)
y11
C
CI
I<3oo Hz
<300 Hz
(4.3)
where
cIl
If<300 Hz
(CPF + CToc)CCAV
CT
CPF + CCAV+ CTOC
(4.4)
At frequencies between 600 Hz and 2 kHz, the pars flaccida admittance is mass domi-
134
(a) Gerbil B8
(b)Gerbil B9
11--
010
O
0o
0
C.)
-10
E
th
0)
a)
'0
0
_r -90
0_
2
0
1
3
1
0
4
1
0
Frequency (Hz)
2
1
0
3
1
4
0
Frequency (Hz)
Figure 4-6: The ingredients that compose the input admittance of the broadband middle-ear model, YI. Comparing these individual admittances allows us to appreciate the
quantitative contributions of these acoustic blocks to the overall middle-ear input admittance. To achieve better match between the middle-ear model and the measured
data at higher frequencies, the RLC representation of YTOC is replaced by a broadband
admittance that was computed from Y s (Eqn. 4.2). The measured YI is also plotted
for comparison purpose.
135
nated, and its contribution to the overall input admittance is negligible. In this range,
Y, is still compliance controlled, where the overall compliance is now simply the series
combination of CCAV and CTOC.
YI
CCAVCTOC
CCAV + CTOC
j
600<f<2000
Hz
(4.5)
Between these two frequency ranges, the middle-ear input admittance exhibits a resonance that is mainly influenced by the RLC behavior of YPF. Together with contributions from CTOC and CCAV, they form the overall input admittance:
yI
Y = (YPF + jWCToc)jwCCAV
1300<<600 Hz
YPF + jW(CTOC + CCAV)
(4.6)
(4.6)
Not surprisingly, the "broad-band" circuit of Figure 4-5 models the measured admittance well at frequencies above 2 kHz, since this is the range where YTOC is the major
contributor to the admittance.
We also fit the single seven-parameter model of Figure 4-3 to the data measured
after opening the bulla hole. For these measurements, one additional step was needed
to estimate the mass and resistance values of the probe tube hole (RHOLE and LHOLE).
These two parameters are related to the size of the hole, and are constrained by the
following equations [Beranek (1986)]:
RHOLE = P
wrr 2-
r
+ 2(
0
2 x 10-3
rhoo(l + 1.75r)
7rr
LHOLE -=
r3
/
(4.7)
(4.8)
2
where v = 1.56 x 10- 5 m 2 /s is the kinematic velocity of the air, I = 0.3 x 10- 3 m is the
136
thickness of the bulla wall, and r is the radius of the bulla hole. For these measurement
sets, the RILC values of the pars flaccida and pars tensa-ossicular-cochlear complex were
first determnined without the bulla hole parameters. RHOLE and LHOLE were then added
to the model, and their values were chosen by varying r to obtain the best model fit for
frequencies between 2 and 5 kHz.
were found to be
The final values of r for both gerbil B8 and B9
0.5 x 10- 3 m, very similar to the physically measured hole radius of
0.6 x 10-3r.
(a) Gerbil B8
(b) Gerbil B9
0O
1-1
U)
0 10
0
o)10
CZ)
E
0
90
a)
"0
a)
0
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure 4-7: Comparison of the input admittances yHO and yHO measured in gerbils
B8 and B9 with the input admittances of the middle-ear circuit model. Again, the model
admittances at frequencies lower than 4 kHz match well with the measured values, but
the high frequency prediction fail to follow the measured trends.
Figure 4-7 shows the best admittance fits to the yHO and yHO measurements made
137
in the right ears of gerbil B8 and B9. The corresponding model parameters are tabulated
in the last two columns of Table 4.1. Since these are independent measurements made in
the same ears as the middle ear intact cases, their respective parameters can be compared
to test the validity and consistency of our circuit model. From Table 4.1 we see that
all three parameters of the pars tensa-ossicular-cochlear complex are consistent across
all four measurements. For the pars flaccida, however, only the compliance parameter
displays good consistency. The damping and masslike properties of the flaccida (RPF and
LPF) show changes that are as large as 60% of their original values. Note that these two
parameters are the ones that are most likely to be affected by the drying and moistening
of the tympanic membrane. In Section 3.1.3, we showed that moistening the tympanic
membrane was able to restore some of the low frequency (presumably pars flaccida's)
compliance, whereas the increase in damping could not be restored. Furthermore, since
drying and moistening of the tympanic membrane could affect its overall mass (especially
the thicker pars flaccida), the revelations that LPF varied moderately from measurement
to measurement should not be surprising.
The same model fitting technique was used to fit the simple circuit model to measurements in B8, B9, B10, and Bl1 made with the middle ear widely opened. In this
configuration, the model has its middle-ear cavity "shorted out" (i.e. second switch set
at position "2"). The resulting model admittances and parameter values are shown in
Figures 4-8, 4-9, and Table 4.2. As was explained in Chapter 3, widely opening the bulla
wall does not eliminate entirely the acoustic effect of the middle-ear cavity. Rather, the
masslike property of the bulla opening interact with the remaining cavity to provide a
high frequency resonance. The size of this irregularly-shaped bulla wall opening was not
measured, and its effect was not included in the model.
138
(b)Gerbil B9
(a) Gerbil B8
C
0
4l
01
0
C',
E
0)
V
E
C:
(A
ell
--
L...
a,
"!
0
CZ
-
-90
10 2
10
Frequency (Hz)
10 4
10
10
104
Frequency (Hz)
Figure 4-8: Comparison of the input admittances yWO and YW O measured in gerbils
B8 and B9 with the input admittances of the middle-ear circuit model. Note the measured impedances show a sharp dip at approximately 6 kHz that is not represented in
the circuit model. Such feature is the result of the resonance between the acoustic mass
of the widely-opened middle-ear hole and the compliance of the middle-ear cavity; the
middle ear model assumes that such a hole is large enough that it shorts out the cavity
compliance, and no resonance is predicted.
139
(a) Gerbil B10O
(b)Gerbil B11
Co
0
O
Cn
0
E
CD1
C0
Eo
E
'COo
o
wD
w
a)
a)
'a
CO)
C13
.C
C-
-90
100
1000
100
1000
Frequency (Hz)
Frequency (Hz)
Figure 4-9: Model fit of the middle-ear input admittance of gerbils B10 and Bl1 - yWO
and Y•O. The measurements were made in the left ears of gerbil B10 and B11 with
the tone-sweep paradigm designed for cochlear potential measurements (see Section 2.4).
As a result, the frequency resolution of these two input admittance plots is substantially
lower than the other results presented in this section.
Measurement
configuration
CTOC (10-12 m 3 /Pa)
CPF (10 - 12 m 3 /Pa)
RTOC (10' Pa-s/m5 )
RpF (10 7 Pa-s/m5 )
LTOC (10 3 kg/m 4 )
LPF (10 4 kg/m 4 )
B8
(Left Ear)
Middle ear
wide open
B9
(Left Ear)
Middle ear
wide open
B10
(Left Ear)
Middle ear
wide open
Bl1
(Left Ear)
Middle ear
wide open
2.1
2.2
1.8
2.9
2.3
2.3
3.5
7.6
2.1
5.8
4.8
2.5
2.2
1.9
1.8
0.9
8.5
6.7
6.8
7.1
7.2
4.5
2.4
7.3
Table 4.2: Middle-ear model parameters. These model parameters were calculated from
the admittance measurements made with the middle-ear cavity widely opened.
140
Similar to the input admittance of the intact middle ear, the low-frequency admittances of yHO and yWO can be approximated using the RLC's values shown in Table 4.2. For both cases, the acoustic admittance of the middle-ear cavity is negligible at
frequencies below 2 kHz. Consequently, below the pars flaccida resonance, we have:
yHO f<3
f<
3 00
z - yWO<3o
z
jw(CPF + CTOC)
(4.9)
f< 3 oo lHz
Hz
At frequencies above the low-frequency resonance (,600 Hz), the pars flaccida admittance is mass dominated, and its contribution towards the overall input admittance is
also negligible. Thus, we have:
YHO
600<f<2o000oo Hz
yWO
W
600<f<2oo000
Hz
jWCToC
(4.10)
In the frequency region where the pars flaccida resonates, the input admittance can be
adequately described by the RLC circuit of the pars flaccida in parallel with CToc:
YPF +JwCTOC
= yHO
yHO
3oo<f<6oo00 Hz
(4.11)
3oo<f<6oo Hz
With the use of these five simple parameters, we were able to accurately describe
the low frequency behaviors (50 Hz< f <2 kHz) of the gerbil middle-ear input admittances, as illustrated in Figures 4-7-4-9. Specifically, we have quantitatively described
the admittance contributions from the pars flaccida, the middle-ear cavity, and the pars
tensa-ossicular-cochlear complex. Table 4.3 shows a summary of all the middle-ear model
parameters discussed in this section in terms of their means and standard deviations.
141
Model param
CTOC (10-12 m
CPF (10- 12 mrn3
RTOC (107 PaRPF (10' Pa-s
LTOC (103 kg/r
LPF (10' kg/mr
CCAV (10
-
12 m
Table 4.3: Means and standard deviations of middle-ear model parameters. The results
in this table are computed from all circuit parameter values presented in Tables 4.1 and
4.2.
4.3
Middle-ear pressure levels-model vs measurements
Having computed the parameters of the middle-ear model, we can test the validity of
its implications by comparing its predictions with measurements that can be determined
experimentally.
One important quantity in the middle-ear sound transmission process is the pressure
ratio (dB difference) across the tympanic membrane. Since this pressure ratio is considered the effective driving force for ossicular motions, any factors that modulate this
ratio can have a significant impact on the hearing process.
Figure 4-10 shows the simple circuit model predictions of the middle-ear to ear-canal
pressure ratio in the middle ear intact configuration. The basic features of these measurements have been discussed in Section 3.1.8 and will not be repeated here. Suffice it to say
that the close agreement between the circuit model predictions and the measurements
at low frequencies confirms the voltage divider principle expressed by Equations 3.3 and
3.4.
An important corollary to such confirmation is the validity of the series model topology, which forms the basis of the voltage divider principle. Results in Figure 4-11, where
142
(a) Gerbil B8
(b) Gerbil B9
10
0
O
L10
°
U)
CL
C,)
U.
C)
(D
(
CO)
COl
0
-90
a-1
100
1000
100
Frequency (Hz)
Figure 4-10: Predictions of
intact configuration-circuit
circuit model and the actual
predictions are based on the
1000
Frequency (Hz)
middle-ear to ear-canal pressure ratio in the middle ear
model. The pressure ratio predicted by the low-frequency
pressure ratio measurements are shown in this figure. The
model parameters determined in the previous section.
143
(a) Gerbil B8
(b) Gerbil B9
1
0
w
'aO
CL
CL
0
"-10
CO)
CO
0)
L,.
U)
(D
,en
CO
C
-..
-90
a"-180
100
1000
100
1000
Frequency (Hz)
Frequency (Hz)
Figure 4-11: Broadband model predictions of middle-ear to ear-canal pressure ratio in
the middle ear intact configuration. At frequencies below 2 kHz, both the broadband and
circuit models are similar to the actual measured pressure ratio. At higher frequencies,
the prediction based on the broadband model is superior to the low-frequency circuit
model when compared with the measured data.
144
the broadband YTOC replaced the simplistic RLC representation, show good agreement
between the broadband model predictions and the measured data at frequencies up to
8 kllz. These results suggest that the range of the series model can actually be extended
to frequencies above 5 kHz, where the pressure measurements in the ear canal and the
middle-ear need not be in phase.
In this case, the voltage divider equations (Equa-
tions 3.3 and 3.4) should be generalized such that the division is based on the overall
admittances of the acoustic blocks rather than their low-frequency compliance values:
IPMECI
_
IPECI PF stiffened
YTOC
YTOC + YCAV
(4.12)
and
IPMECI
IPECI
4.4
TM undisturbed
YTOC+ YPF
YTOC + YCAV + YPF
(4.13)
Effects of Pars Flaccida manipulations on the input to
the inner ears -
bulla wall widely open
Results in the last section (Figures 4-10 and 4-11) show that the decrease in middle-
ear pressure of approximately 3-8 dB at frequencies below the pars flaccida resonance
( 500 Hz) seen after stiffening the parsflaccida is consistent with our model predictions.
In this section, we will discuss whether this change in pressure difference across the
tympanic membrane actually affects the input to the inner ear.
Based on the ear-canal pressure measurements made in the left ears of gerbil B10
and Bl1 (Figures 3-17 and 3-18), along with the middle-ear parameters estimated from
the admittance data (Figure 4-9), we can predict the input to the inner ear based on
the volume velocity entering the pars tensa-ossicular-cochlear complex, UPT, with the
145
(a) Gerbil B10O
(b) Gerbil B11
10
0
0
1-.
80
CO
0)290
0
-s90
-C
a-180
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure 4-12: Comparison of the measured cochlear potentials in gerbils B10 and Bl1 with
the model predictions. The model cochlear potentials shown in this figure were calculated
as the scaled volume velocities entering the pars tensa-ossicular-cochlear complex, with
measured ear-canal pressure levels as the input to the model. The scaling constant was
arbitrarily chosen such that both the model and the measured cochlear potentials are
approximately equal in magnitude throughout the entire spectrum.
146
assumption that these two quantities are proportional to each other. In practice, we used
the cochlear potential recordings as a means of measuring the volume velocity entering
the inner ear, as was explained in Chapter 3.
Figure 4-12 shows a comparison of the experimentally measured cochlear potentials
with the model predictions. The magnitudes of the model predictions were arbitrarily
scaled such that both the model and the measured cochlear potentials are approximately
equal throughout the entire spectrum. Based on the middle ear model, where the pars
flaccida is assumed to be independent from the pars tensa, a change in the pressure difference across the tympanic membrane should produce a proportional change in the volume velocity entering the inner ear. The proportionality constant (or transfer function),
' should be equal to the admittance of the pars tensa-ossicular-cochlear
E-pMT
(PEC-PMEC)
complex, YTOC, independent of the condition of the pars flaccida [see Figures 3-20
and 4-16]. Since the measurements in gerbils B10 and B11 were made with the middle
ear widely opened, IPECI » IPMECI for all frequencies where cochlear potentials were
measured (f < 5 kHz); therefore it is acceptable to ignore the sound pressure level in the
middle ear cavity. From the ear-canal pressure level measurements in Figures 3-17 and
3-18, we would expect that at frequencies below the pars flaccida resonance (; 600 Hz),
the increase in sound pressure levels which result from stiffening pars flaccida should
cause a similar increase in the input to the inner ear. The thicker curves in Figure 4-12
express this fact in the form of the modeled cochlear potentials before and after stiffening
the pars flaccida. Comparing these predictions with the measured cochlear potentials
shows some similarities but also some differences. The measurements show the expected
increases in cochlear potential production at frequencies below 600 Hz, and few changes
at higher frequencies. The actual shape of the measured spectra, however, are different
147
than the predicted values. At low frequencies (f < 200 Hz), the measured cochlear
potentials show a steeper slope than expected, indicating a possible filtering mechanism
that has sharper low-frequency cutoff than simply the transfer function based on admittance YTOC. A possible explanation for this phenomenon is the helicotrema effect on
the cochlear response, which is known to reduce low-frequency sensitivity by reducing
the pressure gradient across the basilar membrane (Dallos, 1970). Another observable
difference between the measured and the model responses is the rate of change of the
phase angles, where the model predicted a faster rate that the actual measured cochlear
potentials. Since the rate of phase angle decrease is directly proportional to the number
of poles minus the number of zeros of the transfer function, this result suggests that the
model circuit contains a greater number of poles with respect to zeros than the data
would indicate. At other frequencies, the observed differences in magnitude are more
difficult to explain because of the uncertainty in the absolute values of the model predictions. These differences, however, are due mostly to our naive RLC representation of the
far more complex ossicular to cochlear transmission process. This limitation, however,
does not pose any serious problem in the current study. Since our points of interest are
to test the validity of the parsflaccida model and its topological connection in the overall
middle-ear model, it is sufficient to know only the difference in cochlear potential productions in ears with normal tympanic membranes and ears with pars flaccida stiffened,
not the actual mechanism of cochlear potential generation. We therefore quantified the
effects of pars flaccida stiffening on the middle-ear input admittance, ear-canal sound
pressure level, and cochlear potential generation in terms of the ratio between the preand post-stiffening results, which are denoted by AY, APEcIv, and ACPjv respectively
(The subscript V is used to indicate that constant voltage was applied to the earphone
148
in the measurement process).
ACPIv = 20log CPIFS,constant v
APEcIV = 20log
Cpconstant V
(4.14)
SI FS,constant V
(415)
PIconstant V
AY= 20 log
Y
YIFS
(4.16)
The changes in cochlear potential and sound pressure level were obtained by taking the
ratio (in dB) between the measurements made in the stiffened ear and the measurements
made in the normal ear. For AY, the order of division was reversed. This is due to the
fact that increasing admittance actually decreases sound pressure level as well as cochlear
potential response. Such analysis would thus show the quantitative contributions of the
pars flaccida to each of these quantities, making it possible to test the modeling of pars
flaccida in the context of the circuit model, but without the complexity of the pars tensa,
ossicles, and cochlea.
Figure 4-13 shows a comparison between the predicted and measured AY, APEC v,
and ACPIv. For gerbil Bl1, the model predictions and the measured responses are
essentially identical from 50 Hz to 10 kHz. Such results support our assumption that
the pars flaccida is an independent shunt path in parallel with the main transmission
mechanism of the middle ear (i.e. the pars tensa-ossicular-cochlear pathway). In other
words, if we assume the ear is listening to a constant volume velocity sound source (as in
the case of our experimental setup), the presence of pars flaccida (as opposed to an ear
with stiffened pars flaccida) provides an additional path for the sound volume velocity at
frequencies below its resonance frequency -
region where its admittance is comparable
to that of the pars tensa [see Figure 4-15]. Consequently the pressure generated at the
149
(a) Gerbil BO10
(b) Gerbil B11
10
2
10
3
10
4
Frequency (Hz)
Figure 4-13: Comparison of the predicted and measured AY, APEc Iv, and ACPIv
in ears with middle ear open. The model calculations do not take into account the
loading effects of the source internal admittance, thereby making the assumption that
lYgerbilear » lYinternalI. As a result, all predicted changes (AY, ACP,andAPEc) are
identical (see the discussion in Section 3.2.2).
150
ear canal is decreased. The amount of sound level decrease (in dB) should thus be exactly
the same as the change in admittance between normal and pars flaccida-stiffened ears. In
addition, if the a.ssumption is correct that pars flaccida and pars tensa are independent,
the decrease in the input to the inner ear (in dB) should also be identical to the change
in ear-canal sound pressure level (recall that
TEýC
is independent of the pars flaccida
when the middle ear cavity is widely opened). Quantitatively, we would expect:
APEcIV = AY = ACPIv = 20log
Y
TOC+ YPF
YTOC
(4.17)
This was exactly what we measured in gerbil Bl1. Results in Gerbil BO10 (Figure 413a), however, show a small frequency region where this assumption is not entirely
accurate.
Between 300 Hz and 600 Hz, the measurements show a significant increase
(up to 20 dB) in cochlear potential that cannot be explained by our circuit model.
This region incidentally also exhibits some expansive nonlinearity in cochlear potential
production (see Section 3.2.1).
resonates.
In addition, it is also the region where pars flaccida
Therefore, this inconsistency could possibly be a result of the interactions
between the pars tensa and the pars flaccida in the acoustic transmission process. The
feasibility of such an explanation required further investigation.
Figures 4-14 and 4-15 provide a test of our circuit model concerning two important
points raised in the above discussions. Figure 4-14 shows the CP transfer functions
P EC
measured in gerbils BO10 and B11 after stiffening the pars flaccida, along with a scaled
version of our model prediction, which in this case is simply the admittance YTOC
(shown in the figure as the measured YwO). Figure 4-15 shows the model and measured
CP transfer functions for ears with normal tympanic membrane and ears with stiffened
UT
151
(a) Gerbil B10O
(b) Gerbil B11
0_
L 10 3
(D
0L
=.
0
2
i-
a) 10
4CO)
C:
as
1---
I,'b
Val
CD
0)
aY)
a 0
CD
UJ)
Cz
03_
.-
-90
10
2
10
10
10
Frequency (Hz)
Frequency (Hz)
Figure 4-14: Comparison of the measured input admittances yWO,
FS model input admitmeasured with the flaccida
tances YWO ,and the middle-ear transfer functions
t eECFS
mesue w t f
stiffened. The admittance plots are scaled relative to the transfer ratio measurements to
obtain a good visual match.
152
pars flaccida. For both figures, it is apparent that the model is unable to represent
the fine structures of the experimentally measured transfer functions. For example, the
model
UT
transfer function does not account for any ossicular slippage or non-planar
vibration of the tympanic membrane (see Section 4.2.1); therefore, it predicts a constant
transfer function that is frequency independent, substantially different than the actual
measurements. Nonetheless, all the basic features observed in these two figures agree
with the discussion presented in the previous paragraphs. In particular, both the model
and the measured CP
a t eEd
C FS
are compliance dominated at low frequencies; the magnitude
increases with frequency, and the phase angle is close to +900.
Both transfer functions
peak at approximately 2 kHz, and they both roll off at higher frequencies. For the CP
transfer function, the most important feature, at least for the purpose of determining the
topology of the pars flaccida, is the difference between measurement made in a normal
ear and measurement made in ear with pars flaccida stiffened. Figure 4-15 shows that
in this regard, both the model and the measurements agree with each other for most of
the frequency range, as is indicated in Figure 4-13.
4.5
Prediction of the effects of Pars Flaccidamanipulations
on the input to the inner ears -
intact bulla wall
When the bulla wall is intact, the addition of the middle-ear cavity changes some of
the behaviors described in the last section. In particular, the middle-ear sound pressure
level is now a significant portion of the ear-canal sound pressure level (see Figure 4-10).
The CP transfer function (with middle ear intact) is no longer simply proportional
to YTOC, rather it depends on all three acoustic blocks in the middle-ear model-
153
(a) Gerbil B1 O
(b) Gerbil B11
CI)
E
E
1., 2
C 10
-101
0
CO
180
(I)
C
•
0
-90
CO-180
'a
S?900
C') -90
-180
100
1000
100
1000
Frequency (Hz)
Frequency (Hz)
Figure 4-15: Comparison of the model and measured CP/UT transfer functions in
gerbils B10 and B11. The measured volume velocities of the entire tympanic membrane
UT were computed as the product of the measured input admittances and measured
ear-canal sound pressure levels. The model transfer functions were scaled in magnitude
to allow visual comparison of the predictions and the experimental data.
154
YTOC, YCAV, and YPF:
CP
I
YTOCYCAV
YPF+ YTOC + YCAV
PEC
__
CP WO)
PEC
YCAV
(4.18)
YPF + YTOC + YCAV
I
where
P
represents the transfer admittance of sound pressure level in the ear-canal
to the volume velocity entering the pars tensa-ossicular pathway with the middle ear
intact. Stiffening the pars flaccida should simply remove the YPF term from the above
equation.
Figure 4-16 shows the predicted
P transfer functions for gerbils BO10 and B11
under various middle ear conditions. The predictions are based on the admittance measurements shown in Figure 4-9. Intuitively, the main effect of the middle ear cavity
is to reduce the pressure difference across the tympanic membrane (i.e. by increasing
the pressure in the middle ear cavity), thereby decreasing the volume velocity entering the inner ear and the production of cochlear potential. Such effect is indeed what
is predicted in Figure 4-16. At frequencies below 3 kHz, the transfer function of ears
with intact middle-ear cavity is substantially decreased when compared to ears with
widely opened bulla walls. In addition, the presence of pars flaccida causes a further
decrease in the transfer function at frequencies below the pars flaccida resonance. All
these phenomena can be readily explained using Equation 4.18. At frequencies above
3 kHz, IYCAVI > IYTOCI > IYPFI; Equation 4.18 thus predicts that
P is the same
with or without the middle ear cavity. Below 3 kHz but above the flaccida resonance
( 500 Hz), IYCAVI and
|YTOCI are of same order of magnitude,
and they are both sub-
stantially greater than IYPFI. Consequently, Equation 4.18 predicts an approximately
6 dB drop in the transfer function of the intact middle ear. At even lower frequencies,
155
(a) Gerbil B10O
(b)Gerbil B 11
3
13-10
3
io
0
2
(1)
4--
C
CL
10
010
1i
n
90
0
-90
-IOU
10 2
10 3
10 4
102
103
10
Frequency (Hz)
Frequency (Hz)
Figure 4-16: Predictions of the effects of middle-ear cavity and tympanic membrane
manipulations on the middle ear transfer functions ( -) of gerbils B10 and B11.
The predictions are based on the circuit model shown in Figure 4-3, where cochlear
potential is assumed to be directly proportional to volume velocity entering the pars
tensa-ossicular-cochlear complex. The magnitudes of all transfer functions were scaled
such that their numerical values are comparable to that of the measured transfer function
(Figure 4-14).
156
|YPF| is comparable to both IYCAV| and IYTOCI, which causes a further reduction in
the transfer function magnitude.
In our experimental setup, the volume velocity entering the middle ear was held
constant (the earphone acted as a volume velocity source when driven by a constant
applied voltage). In this scenario, the middle-ear model predicts that the pars flaccida
acts as a current divider, irrespective of the middle ear condition (Figure 4-17). Thus,
at frequencies where the admittance of the flaccida is significant, volume velocity entering the cochlea is proportionally reduced according to this current divider principle.
Consequently, with or without the middle ear cavity, the changes in cochlear potential
production between ears with normal tympanic membrane and ears with pars flaccida
From our results in the last section, we would
stiffened are the same (Figure 4-18).
expect:
ACP
I
U
=
=
ACP
WO
U
=
=AY
wo
=
-
APEc
WO
U
= 20 log
YTOC+YPF
(4.19)
(4.19
YTOC
The subscript U indicates that the predicted quantity is calculated with the assumption
that the ear is excited by a constant current source (which is approximately equal to
the quantity calculated from experimental measurements obtained with constant voltage
applied to the earphone). With the middle ear cavity intact, AY
-I
-
and APEc
I
U
differ
from those observed in ears with middle ears widely opened. Quantitatively, it can be
shown from the model that:
AY Y
==
C
20 log
+ YTOC)(YCAV +YTOC)
ec
=20
log (YpF
PIu
(YPF + YCAV + YTOC)YTOC
(4.20)
(4.20)
At frequencies where IYpFI < IYTOC+YCAVI (i.e. f > 2 kHz), Equation 4.20 reduces
157
(a) Gerbil BO10
(b) Gerbil B11
2
CE
El
Co
E100
C0
C)
O 90
a)
$D
CD -r-
0-
-90
102
10
10 4
Frequency (Hz)
102
10
10
Frequency (Hz)
Figure 4-17: Predictions of the effects of middle-ear cavity and tympanic membrane
manipulations on the transfer function (cP) of gerbils B10 and B11. The predictions
are based on the circuit model shown in Figure 4-3, where cochlear potential is assumed
to be directly proportional to volume velocity entering the pars tensa-ossicular-cochlear
complex. The magnitudes of all transfer functions were scaled such that their numerical
values are comparable to that of the measured transfer functions (Figure 4-15).
158
(a) Gerbil B10
20 -
10 -
0
AY
-
-10
-
-ACPI,
APEC IU
AlA
WO
ACPI
A
A WO
WO
AYI,A APEC I
(b) Gerbil B11
10
2
10
3
Frequency (Hz)
10
4
Figure 4-18: Predictions of the role of the middle-ear cavity on the effects of stiffening
pars flaccida. This figure shows the predicted AY, ACP, andAPEc for ears with middle
ear intact and ears with middle ear widely opened. The parameters used for the prediction calculations were obtained from acoustic measurements in gerbil BO10 and Bl1. The
theoretical calculations are based on the circuit model shown in Figure 4-3, and do not
take into account the loading effects of the source internal admittance, thereby making
the assumption that IYgerbil earl > IYinternall •
159
to Equation 4.19, indicating their insensitivity to the cavity condition. At lower frequencies, where IYpFI is significant, closing the cavity decreases both AYI' and APEcI.
The model therefore predicts that in ears with middle ear intact, the presence of pars
flaccida causes very little change in middle-ear input admittance and ear-canal sound
pressure level under our. experimental condition. This is true because the presence of the
middle-ear cavity desensitizes the dependence of input admittance and ear-canal sound
pressure level on the pars flaccida. This argument holds true even at low frequencies
where the admittance of parsflaccida is significant (as shown in Figure 4-18). However,
the presence of parsflaccida does affect the middle-ear transmission process. With a constant volume velocity source, the presence of pars flaccida decreases the volume velocity
entering the pars tensa-ossicular pathway according to the current divider principle. This
shunt path mechanism is independent of the middle ear condition.
In general, however, the environmental stimulus is considered to be a constant sound
pressure source, not a constant current source. Under this condition, the mechanism of
how pars flaccida affects the middle-ear transmission process is different than the shunt
path mechanism discussed in the previous paragraph. Under this condition, both our
model and our data suggest that the presence of pars flaccida has only a small effect
on middle-ear sound transmission when the bulla wall is widely opened (see Figure 320). When the middle-ear cavity is intact, the presence of pars flaccida serves to reduce
the pressure across the tympanic membrane at low frequencies (Figure 4-10), thereby
lowering the driving force on the pars tensa. This has the effect of reducing the acoustic
transmission to the inner ear, thus correspondingly reduces the hearing sensitivity. The
amount of reduction in hearing sensitivity due to the presence of pars flaccida, however,
depends on whether the stimulus is considered a constant pressure source or a constant
160
current source. Using the pressure source assumption, the circuit model predicts that the
reduction in cochlear potential generation (which represents the volume velocity entering
the inner ear) due to the presence of pars flaccida is:
ACP
P
= 20 log
TOC + PF + C
YTOC + YCAV
(4.21)
Correspondingly, a constant pressure source forces PEC to be the same in all ears regardless of the condition of the pars flaccida. Therefore APE'I
= 0.
P
Comparing
-I
Equation 4.21 with Equation 4.19 shows that ACPI is reduced when the stimulus is
assumed to be acting as a constant pressure source, indicating that the effect of pars
flaccida on middle-ear sound transmission is smaller when the ear is exposed to envi-
^I
ronmental stimulus. Figure 4-19 compares the two ACP
across the entire frequency
spectrum.
12
8
t
4
CC
0
-4
10
2
10
3
Frequency (Hz)
10
4
Figure 4-19: Effect of using different types of stimulus sources on ACP . The predictions shown in this figure were calculated using the model parameters of Table 4.3. At
frequencies above 600 Hz, the difference between the two curves is small. At lower frequencies, the reduction of volume velocity entering the inner ear is approximately 3 dB
larger when the ear is excited by a volume velocity source.
161
162
Chapter 5
Summary
Results from our acoustic and physiological measurements show that the sound transmission effect of gerbil parsflaccida can be accurately modeled by an RLC circuit. Below
its resonance frequency (e 300-800 Hz), pars flaccida is compliance dominated. Its admittance magnitude in this frequency range is similar to that of the middle-ear cavity
and the pars tensa. Above this high-admittance resonance, the pars flaccida is primarily
mass dominated. ]In this frequency range, its admittance magnitude is significantly lower
than both the middle-ear cavity and the pars tensa-ossicular-cochlear complex.
Our pressure ratio measurements support the common assumption that the middleear cavity acts in series with the main ossicular transmission pathway. Our cochlear
p]otential measurements further illustrate that over most frequency ranges, the movement
of the pars flaccida portion of the tympanic membrane is independent of the pars tensa.
These results are consistent with a middle-ear model having the pars flaccida in parallel
with the combined input admittances of the pars tensa, ossicles, and cochlea.
This
parallel combination could then be connected in series to the admittance of the middleear cavity in accordance with the traditional middle-ear model. In one of our two cochlear
163
potential measurements, significant deviation from this general model was observed in
the 300-600 Hz range, where cochlear potential generation was unexpectedly suppressed
at low sound intensities.
The cause of this deviation is unclear and requires further
investigations.
Results in this study thus provide evidence that over most frequency ranges, the
movement of the pars flaccida does not participate directly in eliciting ossicular motion.
However, the presence of pars flaccida provides a shunt path for the acoustic volume
velocity to enter the middle ear cavity. At low frequencies, where the admittance of pars
flaccida is comparable to that of the pars tensa, the increase in middle-ear pressure due to
this extra shunt path reduces the pressure difference across the tympanic membrane (by
as much as 3-10 dB in gerbil), thereby lowering the driving force and input to the inner
ear. The presence of pars flaccida therefore reduces low frequency hearing sensitivity.
164
Appendix A
Summary of the experimental
measurements
Date
Animal/
Weight
Ear
Description
10/27/94
Al
67 g
L
Healthy ear. Practice the acoustic and cochlear potential
measurements using the high frequency source. Learn
the gerbil anatomy.
12/22/94
A2
47.3
L
Healthy ear. Both hfs and lfs were used. All measurements
were made with the chirp stimulus. Measured the input
admittances, cochlear potentials, and middle-ear pressures
with the tympanic membrane undisturbed, pars flaccida
stiffened, and pars flaccida removed. All measurements
were repeated in both the middle ear intact and bulla hole
open configurations.
L
Healthy ear. Only the Ifs was used. All measurements
were made with the chirp stimulus. The round window
niche and the surrounding areas were filled with fluids,
possibly resulted from a punctured round window membrane.
Measured the input admittances, cochlear potentials,
and middle-ear pressures with the tympanic membrane
undisturbed, pars flaccida stiffened, and pars
flaccida removed. All measurements were repeated
in the middle ear intact, bulla hole open, and middle ear
g
1/5/95
B1
49.6 g
165
widely opened configurations.
1/12/95
B2
L
Healthy ear. Only the Ifs was used. All measurements were
made with the chirp stimulus. With the middle ear widely
opened, we measured the input admittances, cochlear
potentials, and middle-ear pressures in two different
cases - with the tympanic membrane undisturbed,
and with pars flaccida stiffened. Only the
tympanic membrane intact measurements were made
in the hole open and middle ear intact configurations.
Measured the ear canal volume.
59.0 g
1/18/95
B3
51 g
L
Healthy ear. Only the Ifs was used. All measurements were
made with the chirp stimulus. With the middle ear widely
opened, we measured the input admittances, cochlear
potentials, and middle-ear pressures in three different
cases - with the tympanic membrane undisturbed, with
the pars flaccida stiffened, and with the pars
flaccida removed. Only the tympanic membrane intact
measurements were made in the hole open and middle ear
intact configurations. Measured the ear canal volume.
3/1/95
B4
53 g
L
Healthy ear. Both hfs and lfs were used. All measurements
were made with the chirp stimulus. Measured the input
admittances, cochlear potentials, and middle-ear pressures
with the tympanic membrane undisturbed, pars flaccida
stiffened, and pars flaccida removed. All measurements
were repeated in both the middle ear intact and bulla hole
open configurations. Measured the ear canal volume.
3/6/95
B5
65 g
L
Healthy ear. Only the hfs was used. All measurements were
made with the chirp stimulus. With the middle ear widely
opened, we measured the input admittances, cochlear
potentials, and middle-ear pressures in three different
cases - with the tympanic membrane undisturbed, with
the pars flaccida stiffened, and with the pars
flaccida removed. Only the tympanic membrane intact
measurements were made in the hole open and middle ear
intact configurations. Measured the ear canal volume.
3/14/95
B7
66 g
L
Healthy ear. Both the Ifs and hfs were used. All
measurements were made with the chirp stimulus. The
middle ear was widely opened. Measured the input
admittances, cochlear potentials, and middle-ear
pressures with the tympanic membrane undisturbed,
pars flaccida stiffened, and parsflaccida removed.
Most measurements appear leaky. Measured the ear
canal volume.
166
3/14/95
B7
66 g
R
Healthy ear. Both the lfs and hfs were used. All
measurements were made with the chirp stimulus.
Measurements were made with the middle ear intact and
with the bulla hole open. Measured the input admittances,
cochlear potentials, and middle-ear pressures with the
tympanic membrane undisturbed, pars flaccida stiffened,
and pars flaccida removed. Measured the ear canal
volume.
3/20/95
B8
57 g
L
Healthy ear. Both the Ifs and hfs were used. All
measurements were made with the chirp stimulus. The
middle ear was widely opened. Measured the input
admittances, cochlear potentials, and middle-ear
pressures with the tympanic membrane undisturbed,
pars flaccida stiffened, and pars flaccida
removed. Measured the ear canal volume.
3/20/95
B8
57 g
R
Healthy ear. Both the Ifs and hfs were used. All
measurements were made with the chirp stimulus.
Measurements were made with the middle ear intact and
with the bulla hole open. Measured the input admittances,
cochlear potentials, and middle-ear pressures with the
tympanic membrane undisturbed, pars flaccida stiffened,
and pars flaccida removed. Measured the ear canal
volume.
3/22/95
B9
54 g
L
Healthy ear. Both the Ifs and hfs were used. All
measurements were made with the chirp stimulus. The
middle ear was widely opened. Measured the input
admittances, cochlear potentials, and middle-ear
pressures with the tympanic membrane undisturbed,
pars flaccida stiffened, and pars flaccida
removed. Measured the ear canal volume.
3/22/95
B9
54 g
R
Healthy ear. Both the Ifs and hfs were used. All
measurements were made with the chirp stimulus.
Measurements were made with the middle ear intact and
with the bulla hole open. Measured the input admittances,
cochlear potentials, and middle-ear pressures with the
tympanic membrane undisturbed, pars flaccida stiffened,
and pars flaccida removed. Measured the ear canal
volume.
4/24/95
B10
60 g
L
Healthy ear. Only the Ifs was used. All measurements
were made according to the tone-sweep protocol. The
middle ear was widely opened. Measured the ear-canal
pressures and cochlear potentials with the tympanic
membrane undisturbed and with the pars flaccida
stiffened. Measured the ear canal volume.
5/4/95
Bl1
59 g
L
Healthy ear. Only the lfs was used. All measurements
were made according to the tone-sweep protocol. The
middle ear was widely opened. Measured the ear-canal
pressures and cochlear potentials with the tympanic
membrane undisturbed and with the pars flaccida
stiffened. Measured the ear canal volume.
168
Appendix B
Source accuracy charts
This appendix contains the accuracy charts of the low and high frequency sources used
in this thesis. For each source, four different voltage levels were used to drive the earphone. The voltage levels indicated in the following charts refer to the amplitudes of
the linear chirp signals. Four different gray scale levels are used to represent the degrees
of accuracy attainable by the sound source. For instances, the darkest gray scale level
delineate the regions where an unknown admittance can be measured to within 1 dB in
magnitude and 50 in phase; while the lightest gray scale level represent regions where
the errors are either greater than 4 dB in magnitude or 15' in phase. These results were
calculated from 7 sets of measurements over a four month period. Each measurement
set consisted of measurements in 5-6 known acoustic loads whose admittance spanned a
wide range (see Figure 2-10. The errors were determined by comparing the mean of these
measurements with the theoretical admittances discussed in Chapter 2. See Section 2.2.4
for the interpretations and discussions on these accuracy charts.
169
I
_.1..
10j
I I I II
I
I
II
I
I
I
III
I
I
I i 11
I
II
11I
•L•LJLJ•!I
I
I
I
I
I
I
I
ul
I
I
I
L
102
O
0
C0
Ca
o
Cu
.
101
E
10
1 -1 .
10i
102
10 4
Frequency (Hz)
Figure B-1: Source accuracy chart for the low frequency source (driver voltage = 0.32 V).
Four gray scale levels are used to represent the maximum accuracy attainable at the
specified range of admittance magnitude and frequency. For example, the darkest gray
level represents the range over which the source can measure an admittance to within
1 dB in magnitude and 50 in phase. Only the admittance range spanned by the reference
loads is included in this chart. The actual accuracy domain can therefore be larger than
what is shown.
170
I II .I
a
1
*
3
10
liii,
I
I
I
*
I
i
I
i
I
aa
gill
I
I
I
I
I
I
I
I
3
A a
a a I
11111
F
102
CO)
C
0
0
1o
.2
E 101
CD
Co
E
<
-
0
10
10
-1
102
103
10 4
Frequency (Hz)
Figure B-2: Source accuracy chart for the low frequency source (driver voltage = 0.1 V).
Four gray scale levels are used to represent the maximum accuracy attainable at the
specified range of admittance magnitude and frequency. For example, the darkest gray
level represents the range over which the source can measure an admittance to within
1 dB in magnitude and 50 in phase. Only the admittance range spanned by the reference
loads is included in this chart. The actual accuracy domain can therefore be larger than
what is shown.
171
,I aI s I
10
I
i
I
Ili
I
I
I
I I lII
m ii
I
Im
I
Ia
I
I
I
I
I
I
I
I II
i
3
10
C/
0
0Co
4-.
S10
E
~eCd
E
<100
10-1
102
103
10'
Frequency (Hz)
Figure B-3: Source accuracy chart for the low frequency source (driver voltage =
0.032 V). Four gray scale levels are used to represent the maximum accuracy attainable at the specified range of admittance magnitude and frequency. For example, the
darkest gray level represents the range over which the source can measure an admittance
to within 1 dB in magnitude and 5* in phase. Only the admittance range spanned by
the reference loads is included in this chart. The actual accuracy domain can therefore
be larger than what is shown.
172
I I , a II
mliii
I
I
A a I I61311, II
I
I
I
I
I
I
I
I III
I a I11111
I
6
10 3
10 2
10
-
10
-
O
Cz
E
0
0
C'
E
<
10 -1 m
102
10J
104
Frequency (Hz)
Figure B-4: Source accuracy chart for the low frequency source (driver voltage = 0.01 V).
Four gray scale levels are used to represent the maximum accuracy attainable at the
specified range of admittance magnitude and frequency. For example, the darkest gray
level represents the range over which the source can measure an admittance to within
1 dB in magnitude and 50 in phase. Only the admittance range spanned by the reference
loads is included in this chart. The actual accuracy domain can therefore be larger than
what is shown.
173
S
3
10
, , ,,I
aI I
I
I
I
I
.
I
I
I
I I I I
-
10
Cr)
C.O)
M
cn
0
E
-o O
< 10 -
-1
~10 9
10
1u
4
1u
Frequency (Hz)
Figure B-5: Source accuracy chart for the high frequency source (driver voltage =
0.032 V). Four gray scale levels are used to represent the maximum accuracy attainable at the specified range of admittance magnitude and frequency. For example, the
darkest gray level represents the range over which the source can measure an admittance
to within 1 dB in magnitude and 50 in phase. Only the admittance range spanned by
the reference loads is included in this chart. The actual accuracy domain can therefore
be larger than what is shown.
174
a a11.11
I I aI
3
I
a
i
a
l.
a
I
l
1 1
a a taut
I
I
I
I
I
I
I
I
I
I I a I
Email
3
10
10
-
10
()
Co
0
0o
Co
..
10
-
E
C
E
S100 -
10-1 .
102
10J
10 4
Frequency (Hz)
Figure B-6: Source accuracy chart for the high frequency source (driver voltage =
0.01 V). Four gray scale levels are used to represent the maximum accuracy attainable at the specified range of admittance magnitude and frequency. For example, the
darkest gray level represents the range over which the source can measure an admittance
to within 1 dB in magnitude and 50 in phase. Only the admittance range spanned by
the reference loads is included in this chart. The actual accuracy domain can therefore
be larger than what is shown.
175
.
•I , ,,I.1...
.
I
L
.I I
i
LLL11
L1
!
3
3
10
-
2
Cr)
102
10 -
0-'
CO)
0
Co
..e
0(E
o
E
<
"a
10
-
10
-
10
"1
102
10i
10'
Frequency (Hz)
Figure B-7: Source accuracy chart for the high frequency source (driver voltage =
0.0032 V). Four gray scale levels are used to represent the maximum accuracy attainable
at the specified range of admittance magnitude and frequency. For example, the darkest
gray level represents the range over which the source can measure an admittance to
within 1 dB in magnitude and 50 in phase. Only the admittance range spanned by the
reference loads is included in this chart. The actual accuracy domain can therefore be
larger than what is shown.
176
I I
I
l l i
11111
I
I
I
I
I
I
I I I
ll
111111
I
I
I
I
I
I
I
I
I
111111
I II
103
10
2
C'U)
CO)
10
0
0
=3
Ca
10
E
<
100
10-1
102
10 3
104
Frequency (Hz)
Figure B-8: Source accuracy chart for the high frequency source (driver voltage =
0.001 V). Four gray scale levels are used to represent the maximum accuracy attainable at the specified range of admittance magnitude and frequency. For example, the
darkest gray level represents the range over which the source can measure an admittance
to within 1 dB in magnitude and 50 in phase. Only the admittance range spanned by
the reference loads is included in this chart. The actual accuracy domain can therefore
be larger than what is shown.
177
178
Appendix C
Other admittance and pressure
measurements
This appendix contains all the input admittance and pressure ratio measurements obtained in this study, but are not discussed in the thesis. Most of these measurements
were made in the earlier part of the study, where the effects of membranal drying on
acoustic measurements were not fully recognized. Consequently, care was not taken to
prevent the drying of the tympanic membrane, and the results are less consistent than the
measurements obtained in the later experiments. The frequency ranges of the measurements shown in this appendix were chosen in accordance with the discussion presented
in Section 3.1: measurements made with the lfs alone were limited to frequencies below
6 kHz, and hfs measurements below 200 Hz were truncated. The largest frequency range
was obtained from measurements made with both sources, which extend from 50 Hz to
10 kHz.
179
(a) Middle ear intact
10
(b)Bulla hole open
2
C
10
4-1
CI)
0~
ID10
CO
O)
O10
E
*-
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure C-1: The middle-ear input admittances measured in the left ear of gerbil A2.
(a) Measurements made in the intact middle-ear, and (b) measurements made with the
bulla hole open. Three measurements are shown in this figure: 1) with a normal and
undisturbed tympanic membrane, 2) with the pars flaccida stiffened, and 3) with the
pars flaccida removed.
180
(a) Gerbil B1
(b)Gerbil B2
2
0
4 10
O
_0
<E
IU
90
0
-90
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
10
4
Figure C-2: The middle-ear input admittances measured in the left ears of gerbils B1
and B2-middle ears widely opened. For gerbil B1, three measurements are shown in
this figure: 1) with a normal and undisturbed tympanic membrane, 2) with the pars
flaccida stiffened, and 3) with the pars flaccida removed. For gerbil B2, only the first
two measurements were obtained.
181
(b) Gerbil B5
(a) Gerbil B3
10
2
4-'
C.)
0 lO
CO10
E
4-'
4-
E 10lo
VtO
I-
V 0
U)
-C -90
C.
2
Frequency (Hz)
1
2
4
3
0
1
0
1
0
4
3
1
0
Frequency (Hz)
1
0
Figure C-3: The middle-ear input admittances measured in the left ears of gerbils B3
and B5-middle ears widely opened. For gerbil B5, three measurements are shown in
this figure: 1) with a normal and undisturbed tympanic membrane, 2) with the pars
flaccida stiffened, and 3) with the pars flaccida removed. For gerbil B3, only the first
two measurements were obtained.
182
(a) Gerbil A2
(b) Others
C:
0O
.m
10
0
Cz
E
0
C -
E
I
n
90
0
-90
--I U
10
2
10
3
4
Frequency (Hz)
2
10
3
Frequency (Hz)
Figure C-4: Middle-ear cavity to ear-canal pressure ratio measurements. (a) Measurements made in the left ear of gerbil A2. The pressure ratios were measured under three
different conditions: 1) with the tympanic membrane intact and undisturbed, 2) with the
pars flaccida stiffened, and 3) with the pars flaccida removed. (b) Measurements made
in five different gerbils. All measurements were made in ears with normal tympanic
membrane.
183
(a) Gerbil B1
(b)Gerbil B2
CO 10
C
CI)-1o0
=-
010
a
C)
E -2
E10
1in
90
0
-90
-1 80U
10
2
10
3
Frequency (Hz)
10
4
10
2
10
3
Frequency (Hz)
4
10
Figure C-5: Middle-ear cavity to ear-canal pressure ratios measured in the left ears of
gerbils B1 and B2-middle ears widely opened. The pressure ratios were measured under
two conditions: 1) with the tympanic membrane intact and undisturbed, and 2) with
the pars flaccida stiffened.
184
(a) Gerbil B3
(b)Gerbil B5
0
10
Cl)
0)10
010
C.)
Cz
10
CO
4.
C 10
"0
180R
90
0
-90
-90
- I•U
2
10
10
3
Frequency (Hz)
10
4
10
2
10
3
4
Frequency (Hz)
Figure C-6: Middle-ear cavity to ear-canal pressure ratios measured in the left ears of
gerbils B3 and B5-middle ears widely opened. The pressure ratios were measured under
two conditions: 1) with the tympanic membrane intact and undisturbed, and 2) with
the pars flaccida stiffened.
185
186
Appendix D
List of symbols
Most acoustic variables used in this thesis are expressed in the complex frequency domain.
They are printed in bold.
c
propagation velocity of sound (m/sec)
CA
acoustic compliance (m 3 /Pa)
CCAV
acoustic compliance of the middle-ear cavity (m 3 /Pa)
CPF
acoustic compliance of the pars flaccida (m 3 /Pa)
CTOC
acoustic compliance of the pars tensa-ossicular-cochlear complex (m 3 /Pa)
CP
cochlear potential (volt)
ACP
ratio of pre- and post-stiffened cochlear potentials: 20 log CI
APEc
ratio of pre- and post-stiffened ear-canal sound pressure levels: 20 log •
AY
ratio of pre- and post-stiffened middle-ear input admittances: 20 log
viscosity coefficient (N - sec/m 2 )
F[k]
discrete frequency spectrum of the chirp stimulus
i(t)
current in time domain (Amp)
J
imaginary number V/I
187
(dB)
Y
(dB)
(dB)
kpt
complex proportionality constant of probe-tube microphone (volt/Pa)
ks
complex proportionality constant of source microphone (volt/Pa)
A
wavelength of sound (m)
L
inductance (Henry)
LA
acoustic mass (kg/mrn 4 )
LHOLE
acoustic mass of the bulla hole (kg/m 4 )
LK
Karal inertance (Henry)
LPF
acoustic mass of the parsflaccida (kg/m 4 )
LTOC
acoustic mass of the pars tensa-ossicular-cochlear complex (kg/m 4 )
m
normalization constant
w
radian frequency, 27r f (1/sec)
v
kinematic velocity of air (m 2/s)
P
sound pressure level (Pa,N/m 2 )
p(t)
sound pressure level -
PEC
sound pressure level in ear canal (Pa,N/m 2 )
PL
sound pressure level in acoustic load (Pa,N/m 2 )
PMEC
sound pressure level in the middle-ear cavity (Pa,N/m2)
Po
density of air at STP (1.19kg/m
RA
acoustic resistance (Pa - sec/m 5 )
RHOLE
acoustic resistance of the bulla hole (Pa - sec/m 5 )
RpF
acoustic resistance of the pars flaccida (Pa - sec/m 5 )
RTOC
acoustic resistance of the pars tensa-ossicular-cochlear complex (Pa - sec/m 5)
U
volume velocity (m 3 /sec)
UpF
volume velocity entering the pars flaccida (volt -
time domain (Pa,N/m 2 )
188
3
)
m 3
/Pa - sec)
UpT
3
volume velocity entering the pars tensa (volt - m /Pa - sec)
-Us
source volume velocity (volt - m 3 /Pa - sec)
UT
3
volume velocity of the entire tympanic membrane (volt - m /Pa - sec)
v(t)
voltage in time domain (Volt)
YCAV
3
acoustic admittance of middle-ear cavity (S, m /Pa - sec)
YHO
middle-ear input admittance-bulla hole open (S, m 3 /Pa - sec)
YAHO
middle-ear input admittance-middle ear widely open and pars flaccida's
AR
dental shield removed (S, m 3 /Pa - sec)
YHO
middle-ear input admittance-bulla hole open and pars flaccida stiffened
rn 3 /Pa - sec)
(S, m
YI
middle-ear input admittance-bulla wall intact (S, m 3 /Pa - sec)
YIg
middle-ear input admittance-bulla wall intact and pars flaccida stiffened
(S, m 3 /Pa - sec)
YIR
middle-ear input admittance-bulla wall intact and pars flaccida removed
(S, m 3 /Pa - sec)
YL
admittance of acoustic load (S, m 3 /Pa - sec)
YPF
acoustic admittance of the pars flaccida (S, m 3 /Pa - sec)
Y
internal source admittance (S, m 3 /Pa - sec)
YSC
input admittance of the stapes and cochlea (S, m 3 /Pa - sec)
YT
total input admittance of the gerbil middle ear (S, m 3 /Pa - sec)
YTOC
input admittance of the pars tensa-ossicular-cochlear complex (S, m 3 /Pa - sec)
yWO
mniddle-ear input admittance-middle ear widely open (S, m 3 /Pa - sec)
YWO
middle-ear input admittance-middle ear widely open and pars flaccida
FS
Z
stiffened (S, m 3 /Pa - sec)
acoustic impedance (acoustic 9, Pa - sec/m
189
3
Bibliography
Beranek, L. L. (1954). Acoustics. McGraw-Hill, New York.
Cohen, Y. E., Doan, D. E., Rubin, D. M., and Saunders, J. C. (1993).
"Middle-ear
development V: Development of umbo sensitivity in the gerbil," Am. J. Otolaryngol
14(3):191-198.
Dallos, P. (1970).
"Low-frequency auditory characteristics:
Species dependence," J.
Acoust. Soc. Am. 48(2):489-499.
Dallos, P., Cheatham, M., and Ferraro, J. (1974). "Cochlear mechanics, nonlinearities,
and cochlear potentials," J. Acoust. Soc. Am. 55(3):597-605.
Dear, S. P. (1987). Impedance and sound transmission in the auditory periphery of the
chinchilla. Ph.D. thesis, U of Pennsylvania.
Dennis, J. and Woods, D. (1987). "New computing environments: Microcomputers in
large-scale computing," in Wouk, A., editor, SIAM, pages 116-122.
Desoer, C. and Kuh, E. (1969). Basic Circuit Theory. McGraw-Hill Inc., New York.
Diependaal, R., de Boer, E., and Viergever, M. A. (1987). "Cochlear power flux as an
indicator of mechanical activity," J. Acoust. Soc. Am. 82:917-926.
190
Egolf. D. (1977). "Mathematical modeling of a probe-tube microphone," J. Acoust. Soc.
Am. 61:200-205.
Fletcher, N. H. (1992). Acoustic Systems in Biology. Oxford University Press, New York.
Guinan, J. and Peake, W. T. (1967). "Middle-ear characteristics of anesthetized cats,"
J. Acoust. Soc. Am. 41:1237-1261.
Harada, Y. (1983). Atlas of the ear by scanning electron microscopy. MTP Press, London.
HIellstr6m, S. and Stenfors, L.-E. (1983). "The pressure equilibrating function of pars
flaccida in middle ear mechanics," Acta. Physiol. Scand. 118:337-341.
Hutchings, M. (1987). "The gerbil as an animal model of otitis media with effusion," J.
Physiol. (London) 396.
Karal, F. C. (1953).
"The analogous acoustical impedance for discontinuities and con-
strictions of circular cross section," J. Acoust. Soc. Am. 25(2):327-334.
Khanna, S. M. and Tonndorf, J. (1972). "Tympanic membrane vibrations in cats studied
by time-averaged holography," J. Acoust. Soc. Am. 51(6):1904-1920.
Eohll6ffel, L. (1984). "Notes on the comparative mechanics of hearing. iii. On Shrapnell's
membrane," Hearing Research 13:83-88.
Eringlebotn, M. (1988).
"Network model for the human middle ear," Scand. Audiol.
17:75-85.
Lay, D. (1972). "The anatomy, physiology, functional significance and evolution of specialized hearing organs of gerbilline rodents," J. Morph. 138:41-120.
Lynch, III, T. J. (1981). Signal processing by the cat middle ear: Admittance and transmission, measurements and models. Ph.D. thesis, MIT.
Lynch, III, T. J., Nedzelnitsky, V., and Peake, W. T. (1982). "Input impedance of the
cochlea in cat," J. Acoust. Soc. Am. 72(1):108-130.
Lynch, III, T. J., Peake, W. T., and Rosowski, J. J. (1994).
"Measurements of the
acoustic input impedance of cat ears: 10 hz to 20 khz," J. Acoust. Soc. Am. 96:21842209.
Moller, A. R. (1961). "Network model of the middle ear," J. Acoust. Soc. Am. 33(2):168176.
Moller, A. R. (1963).
"Transfer function of the middle ear," J. Acoust. Soc. Am.
35(10):1526-1534.
Moller, A. R. (1965). "An experimental study of the acoustic impedance of the middle
ear and its transmission properties," Acta oto-laryng. 60:129-149.
Nedzelnitsky, V. (1980).
"Sound pressures in the basal turn of the cat cochlea," J.
Acoust. Soc. Am. 68(6):1676-1689.
Neely, S. T. and Kim, D. O. (1986). "A model for active elements in cochlear biomechanics," J. Acoust. Soc. Am. 79(5):1472-1480.
Nelder, J. and Mead, R. (1964). "A simplex method for function minimization," Computer Journal7:308-313.
Nilsson, J. W. (1990). Electric Circuits. Addison-Wesley, Reading, Massachusetts.
192
Pang, X. D. and Peake, W. T. (1985). "How do contractions of the stapedius muscle
alter the acoustic properties of the ear," in Allen, J. B., Hall, J. L., Hubbard, A.,
Neely, S. T., and Tubis, A., editors, PeripheralAuditory Mechanisms, pages 36-43.
Springer-Verlag.
Pickles, J. O. (1988). An Introduction to the Physiology of Hearing. Academic Press, 2
edition.
Ravicz, M. E. (1990). Acoustic impedance of the gerbil ear. Master's thesis, Boston
University.
Ravicz, M. E., Rosowski, J. J., and Voight, H. F. (1990). "Acoustic impedance measurements in the gerbil ear," J. Acoust. Soc. Am. Suppl 1 87:S101.
Ravicz, M. E., Rosowski, J. J., and Voigt, H. F. (1992).
"Sound-power collection by
the auditory periphery of the mongolian gerbil meriones unguiculatus.i: Middle-ear
input impedance," J. Acoust. Soc. Am. 92(1):157-177.
Rosowski, J. J. (1991).
"The effects of external- and middle ear filtering on auditory
threshold and noise-induced hearing loss," J. Acoust. Soc. Am. 90(1):124-135.
Rosowski, J. J., Carney, L. H., Lynch, T. J., and Peake, W. T. (1986). "The effectiveness
of external and middle ears in coupling acoustic power into the cochlea," in Allen,
J. B., Hall, J. L., Hubbard, A., Neely, S. T., and Tubis, A., editors, Peripheral
Auditory Mechanisms, pages 3-12. Springer-Verlag.
Rosowski, J. J., Davis, P. J., Merchant, S. N., Donahue, K. M., and Coltrera, M. D.
(1990). "Cadaver middle ears as models for living ears: Comparisons of middle ear
input impedance," Ann Otol Rhinol Laryngol 99(5):403-412.
193
Rosowski, J. J. and Merchant, S. N. (1995). "Mechanical and acoustic analysis of middle
ear reconstruction," Am. J. Otolaryngol 16(4):486-497.
Rosowski, J. J., Peake, W. T., and Lynch, T. J. (1984). "Acoustic input-admittance of
the alligator-lizard ear: Nonlinear features," Hearing Research 16:205-223.
Ryan, A. (1976). "Hearing sensitivity of the mongolian gerbil, meriones unguiculatis,"
J. Acoust. Soc. Am. 54:1222-1226.
Schmiedt, R. and Zwislocki, J. (1977). "Comparison of sound-transmission and cochlearmicrophonic characteristics in mongolian gerbil and guinea pig," J. Acoust. Soc. Am.
61(1):133-149.
Shaw, E. A. G. (1974). "The external ear," in Keidel, W. D. and Neff, W. D., editors,
Handbook of sensory physiology: Vol V/1: Auditory System, volume 5, chapter 1,
pages 455-490. Springer-Verlag, New York.
Stenfors, L.-E., Salin, B., and Windblad, B. (1979). "The role of the pars flaccida in the
mechanics of the middle ear," Acta oto-laryng. 88:395-400.
Tonndorf, J. and Khanna, S. M. (1970). "The role of the tympanic membrane in middle
ear transmission," J. for Oto-Rhino-Laryngology and its related specialties 79:743753.
von Unge, M., Bagger-Sj6back, D., and Borg, E. (1991). "Mechanoacoustic properties
of the tympanic membrane: A study on isolated mongolian gerbil temporal bones,"
Am. J. Otology 12:407-419.
194
Zuercher, J. C., Carlson, E. V., and Killion, M. C. (1988).
"Small acoustic tubes:
New approximations including isothermal and viscous effects," J. Acoust. Soc. Am.
83(4):1653-1660.
Zwicker, E. (1986).
"A hardware cochlear nonlinear preprocessing model with active
feedback," J. Acoust. Soc. Am. 80:146-153.
Zwislocki, J. (1962). "Analysis of the middle-ear function. Part 1: Input impedance," J.
Acoust. Soc. Am. 34:1514-1523.
Zwislocki, J. (1963). "Analysis of the middle-ear function. Part II: Guinea-pig ear," J.
Acoust. Soc. Am. 35:1034-1040.
195